The correct answer is option 4: "He supported the Age of Consent Bill."

Option 1: Bal Gangadhar Tilak is known for his contribution to Indian nationalism and his efforts to promote self-rule. However, he did not propound the theory of the Arctic Home of the Aryans. This theory was actually proposed by another Indian nationalist named Bal Gangadhar Tilak.

Option 2: Bal Gangadhar Tilak was one of the founders of the Anti-Cow Killing Society. This society aimed to protect cows, which were considered sacred by the Hindu religion, from being slaughtered.

Option 3: Bal Gangadhar Tilak did indeed set up the Home Rule League at Poona. The league was an organization that advocated for self-government and worked towards achieving home rule for India.

Option 4: Bal Gangadhar Tilak did not support the Age of Consent Bill. In fact, he vehemently opposed it. The bill sought to raise the age of consent for marriage for girls, but Tilak argued that it was an infringement on the religious and cultural practices of Hindus.

In conclusion, option 4 is incorrect as Bal Gangadhar Tilak did not support the Age of Consent Bill.