The Emperor's Club

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In 2001, William Hundert, a retired Classics teacher, is flown out to a luxurious resort in the Hamptons owned by one of his former students in order to be the guest of honor in an impromptu reunion. As he gets settled in he reflects on the turn of events in a flashback of his time working at Saint Benedict's Academy, a prestigious preparatory school. Twenty-eight years earlier, a younger Mr. Hundert is enthusiastic about the start of the school year. His class turns out to be a strict yet inspiring lesson for the freshmen. They include laid-back Louis Masoudi, introverted Martin Blythe, and studious Deepak Mehta. Hundert inspires his students to study hard in order to become one of the three contestants for The Emperor's Club and be crowned "Mr. Julius Caesar", an academic competition between top three students of his class regarding the Classics. When the headmaster explains the contest to the students, he mentions that Blythe's father was once a "Mr. Julius Caesar".
Hundert's orderly world is shaken when a new student, Sedgewick Bell, walks into his classroom late. Bell is the cocky son of a senior U.S. senator who possesses none of Hundert's principles. After Sedgewick plays the class clown, Hundert asks him to name a single Roman Emperor. When Bell cannot, Hundert has the other students perfectly recite the line of succession of the Roman Empire. Hundert also makes a trip to Washington, D.C. to meet with Senator Bell. Bell's father is uninterested in his son's character development, telling Hundert just to teach Bell so he can graduate. In a phone call, Senator Bell chastises Sedgewick for wasting his fatherâs time and money. After seeing him chastened, Hundert tries to become a mentor to Bell in order to make him a better man. Bell starts studying and his grades improve. Bell finishes fourth in Hundert's essay competition that precedes the contest, and Hundert raises his grade on the final essay, thus eliminating Blythe. Hundert is caught between celebrating Bell's newfound success and feeling guilty when he sees a despondent Blythe. Hundert is also saddened by the fact that another teacher, with whom he has a growing friendship, is moving to England due to her husband's job.
The entire school watches the competition as the three contestants are quizzed by Hundert. After many questions, Masoudi is eliminated. Hundert becomes increasingly suspicious of Bell raising his toga to his head to think. When Hundert confers with the headmaster, he is urged to give Bell a pass. Hundert instead asks him a question not in the books, "Who was Hamilcar Barca?", knowing full well that the answer would not be on any materials used to cheat (it was not in the curriculum) but knowing that Mehta would be able to answer it. Bell is stumped and Mehta is crowned Mr. Julius Caesar. Afterwards, Bell admits to Hundert that he cheated. Although Hundert does not publicize this, the trust he once had with Bell is broken. After the headmaster of St. Benedict's dies, the Board of Trustees promotes a younger, less experienced teacher (Rob Morrow) to the headmastership based on his abilities to raise funds for the cash-strapped school. Shocked by this turn of events, Hundert retires from teaching.
Meanwhile, wealthy CEO Sedgewick Bell is poised to make a gigantic contribution to St. Benedict's, but only if Hundert comes to a black tie party with all his 1973 students in a rematch of the Mr. Julius Caesar competition. In the immediate present, Hundert has accepted the terms of the contribution. The competition is preceded by a dinner showing his former students in all their success, with an adult Mehta working as a college professor teaching Classics himself. The reunion with Blythe is uncomfortable.
Masoudi is eliminated early. When Hundert notices Bell stumble on a question then recover, he notices that Sedgewick is wearing a tiny earpiece, through which a graduate student is feeding answers to him. Hundert once again asks an obscure question he had previously asked his class back in 1973, "Who was Shutruk-Nakhunte?" The reason for this was mentioned at the start of the school year by Mr. Hundert to his students. He uses the Elamite king as an example of the idea that great ambition and conquest without contribution is meaningless. Bell is stumped and Mehta wins. Immediately after the competition, Sedgewick announces his plans to begin campaigning for the U.S. Senate. Hundert is furious and excuses himself to the restroom where he is met by Bell. Hundert confronts Bell on his cheating. An indifferent Bell says that Hundert has let life pass him by, whereas he will win because he is not restrained by ethics. Seeing Blythe, Hundert confesses to favoring Bell at his expense. Blythe says that it does not matter, but his body language suggests he is upset.
The day after the rematch, Hundert is then greeted by his 1973 students who give him a "surprise breakfast" and present various mementos of their time under his tutelage. Hundert realizes that although he failed with Bell, he has succeeded greatly with other students.
Hundert returns to St. Benedict's and again teaches Classics to a new class (which is now coeducational and more racially diverse than his earlier classes). It is also revealed that one of his students is Blythe's son, who is proud that his father was once Hundert's student. Hundert then looks out the window to see Martin Blythe proudly waving to him, implying that Hundert is forgiven. Hundert requests the Blythe boy read the Shutruk-Nahunte plaque over the door, just as his father once did.

Question: What did Bell raise to his head to "Think"?
Answer: Toga