In '' Brokeback Mountain '' , Gyllenhaal and Heath Ledger play young men who meet as sheep herders and embark upon a sexual relationship that begins in the summer of 1963 and lasts for 20 years . The film was often referred to in the media with the shorthand phrase " the gay cowboy movie " , though there was differing opinion on the sexual orientation of the characters . The film won the Golden Lion prize at the Venice Film Festival . The film went on to win four Golden Globe Awards , four British Academy of Film and Television Arts ( BAFTA ) Awards , and three Academy Awards . Gyllenhaal was nominated for an Academy Award in the category of Best Supporting Actor for his performance but lost to George Clooney for '' Syriana '' . Gyllenhaal also won the Best Supporting Actor BAFTA for the same role and received a Best Supporting Actor nomination and Best Film Ensemble nomination from the Screen Actors Guild . Also for '' Brokeback Mountain '' , he and Ledger won an MTV Movie Award for " Best Kiss " in 2006 . Shortly after the 2006 Academy Awards , Gyllenhaal was invited to join the Academy in recognition of his acting career
MTV Movie Award
2006 MTV Movie Awards
Jake Gyllenhaal