Ledger received `` Best Actor of 2005 '' awards from both the New York Film Critics Circle and the San Francisco Film Critics Circle for his acting in Brokeback Mountain . In this movie he plays Wyoming ranchhand Ennis Del Mar , who is in love with rodeorider Jack Twist , played by Jake Gyllenhaal . Ledger received `` Best Actor of 2005 '' awards from both the New York Film Critics Circle and the San Francisco Film Critics Circle for his performance in Brokeback Mountain , in which he plays Wyoming ranch hand Ennis Del Mar , who has a love affair with aspiring rodeo rider Jack Twist , played by Jake Gyllenhaal .