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— Müller's internal monologue during the final chapter of The Last Tiger
A highly experienced and apparently loyal Wehrmacht officer, Müller is good friends with Kertz, Tiger 237's driver, having known and served with him for several years. The pair affectionately refer to their tank as "Stefan".
Müller is a conflicted character who sees it as his duty to continue the fight against all odds, but also shows some signs of disillusionment with the regime, such as his voicing of discontent over the hanging of their own soldiers and refusal to salute the officer carrying out the sentence. He is shown to be initially tolerant of Schröder, whom he mentors and is idolised by. Kertz criticises Müller for his "feeding [Schröder] the party line", and Müller eventually sees the result of his encouragement taken too far.
Despite declaring that he "tells no lies", much of his inspiring diatribe is increasingly meaningless to him as his resolve to continue fighting crumbles. Kertz, having known him for several years and being very cognisant of the current situation, sees through this facade and confronts him about it during the story finale. Müller is apparently aware of his own lies, but is still resistant to admitting that everything is over until the very end. His determination is finally broken by the fate of his crew.
Although confident in the field, Müller has doubts about his command abilities and hesitates in his decision making several times. When stressed, he has a habit of looking away from others and blinking rapidly, which may be a form of nervous tick. He assumes that there will be a point where he can examine his failures in retrospect and address them, but time for such reflection has seemingly run out. He also describes feeling anxious when outside the tank, as the world outside seems more immediate and harsh when he is exposed to the sights and smells of death. He also recognises that without the machine he is just another "flawed and vulnerable man".
Peter mentions that when he was a boy, he was among a group of boys who stole from a local shop. Despite not taking anything, his father still condemned him for being there.
Müller, along with Kertz, first appear in the prologue My Country Calling, during the siege of Tobruk in 1941. Müller's Tiger fights through a defending British force of Staghound T17E1s, Shermans, 6 Pounder guns and a Sherman Calliope, before artillery hits near the tank and cutting to black.
At the beginning of The Last Tiger, a flashback is shown of Müller ambushing a British mechanised convoy somewhere in North Africa. The tank destroys a Churchill Mk VII, with Müller watching through binoculars as the dismounting crew burn to death before commanding the tank to advance.
The story jumps forwards to the present of Spring 1945, where Müller is taking part in the defense of the Rhine-Ruhr region of Germany. The tank is in need of resupply and is missing its radio operator, consisting of veteran Kertz, young fanatic Schröder and similarly young nervous wreck Hartmann. Schröder idolizes Müller and follows him everywhere, a fact which is mocked by Kertz during the briefing. The Tiger moves out over a bridge across the Rhine, and while Kertz questions their orders amidst the deteriorating strategic situation, Müller flatly states that they are instead pushing forward. They pass a cathedral, where a line of German soldiers, labelled with signs around their necks as "deserters", are escorted at gunpoint. Schröder announces his disdain for the group, while Müller states that Germany is "stronger together".
The tank advances to the front and is attacked by US forces en route to Schimek Railyard. During the battle, he navigates for Kertz and prompts Hartmann to keep in contact with command via radio. After they enter the town square to destroy enemy artillery pieces, the Tiger is counter-attacked by American armor. Müller calmly directs the crew to fight their way out, and they continue to the rally point. On the way, Hartmann has a nervous breakdown and begs for the crew to return to the bridge, to which Schröder responds angrily - Müller asks the two of them to be quiet and do their jobs, remarking that they will be back at the bridge soon enough and reinforcing his belief in the superiority of the Tiger tank.
The crew arrives at the rally point to find they are on their own, before coming under attack from rocket-firing Mosquitos. Kertz drives the tank through a destroyed building to escape danger, requiring someone to leave the tank to scout a path back through the debris. Schröder suggests Hartmann should go, and after much hesitation Müller ultimately agrees, despite Kertz' protests. Hartmann himself pleads not to go, but Müller coerces him by appealing to his sense of duty, and he reluctantly dismounts the Tiger. The crew watches him disappear from view, but with the sudden arrival of an American mechanized column, Müller commands Kertz to leave without Hartmann.
The tank is directed by radio to the German forward base, and is instructed to destroy sensitive documents there. While approaching the objective, the tank is once again attacked by Mosquitos and disabled. Müller orders Kertz to fix the tank while he proceeds on foot to capture an anti-aircraft gun to shoot down the circling attack aircraft. He successfully destroys the Mosquitos, and is reunited with the repaired Tiger after Kertz followed the sounds of gunfire. The tank's radio remains inoperable, severing their connection to command. Proceeding onward, Müller once again dismounts and takes back the intelligence files from the abandoned outpost despite resistance from American guards. Their orders complete, Müller directs the crew to return to the cathedral to take part in the final defense.
On the way, the tank passes through a ruined alley. A propaganda speaker announces that the battle has not been in vain and that Germany cares about is soldiers and citizens, which is hypocritically juxtaposed by Müller's witnessing of wrecked tanks, dead civilians, and the deserters seen earlier, now hanged from lampposts. Kertz stops the tank ahead of an iron gate, causing Müller to look up and see Hartmann, also labelled a deserter and hanged. Schröder reasserts his belief in Hartmann's treachery, causing Müller to snap back at him to shut up, stating that he did his duty. Schröder disagrees, and the tank continues on to the cathedral.
Night has fallen by the time Tiger 237 reaches their objective, which is completely devoid of friendly soldiers. A dismayed Schröder has a minor outburst, which is silenced by Müller, who exits the tank to find a working radio. A hurried transmission orders the crew to defend the bridgehead at all cost, while simultaneously a US tank formation surrounds the church, demanding the crew surrender. Müller appears to be contemplating the situation, before Schröder takes the situation into his own hands, opening fire on the Americans. Müller quickly reembarks, and the crew fights through waves of enemy tanks until heavy artillery begins to dial in on their position. With the situation becoming untenable, Müller directs the tank to withdraw towards the bridge and rejoin the main force. The tank is seconds away from reaching the bridge before an explosion tears through the structure, sending the Tiger careening down an embankment, coming to a rest immobilized in debris.
A disorientated Müller exits through the turret hatch, and gazes forlornly at the burning bridge. Movement behind him causes him to draw his pistol on Kertz who, injured and seemingly at his wits end, is preparing to desert. Müller implores his friend to return to the tank, but apparently has no plan beyond this, which is apparent to Kertz who cuts through his vague words of comfort. Through frustrated tears, Kertz laments about the things they saw and did in service of a regime that has callously abandoned them, while Müller stares on in silence, offering no further opposition as his friend limps away. Suddenly Kertz is cut down by gunfire, and Müller turns in shock to find Schröder having fired the shots. Schröder apologies for having shot his friend, but reasons he was a deserter and a traitor, justifying the action using Müller's earlier stated mottos that they are "stronger together". Müller however, completely ignores Schröder and runs over to comfort his dying comrade.
US soldiers, attracted by the bridge explosion and gunfire, descend on the scene. Schröder immediately opens fire and a gun battle erupts, with Schröder begging his commander to return to the tank. As Kertz dies in his arms, Müller finally decides to give up the fight, discarding his Iron Cross into the dirt beside Kertz' corpse and raising his hands in surrender. Perceiving this as the ultimate betrayal, Schröder screams in anguish and turns his MP40 on his former commander. Gunshots ring out as the screen cuts to black, leaving the fate of Müller and his last surviving crew member ambiguous.