Burt Lancaster did not receive an Oscar nomination, despite receiving a BAFTA nomination, for portraying Felix Happer in Local Hero.
Burt Lancaster plays the owner of the Texas oil company named Felix Happer. Local Hero is a lighthearted style of comedy with many colorful and off-beat characters. The first one we meet is Happer played by Lancaster who we first meet as he's sleeping through a meeting about the refinery in Scotland. Happer then proceeds to send Mac MacIntyre (Riegert) on this particular mission simply because he believes him to be Scottish due to his surname. Happer first gives Riegert a few words of "wisdom" the most important of which is to make sure to look to the sky. Lancaster of course has the command needed to man of Happer's power, but Lancaster wryly portrays the eccentricities of his character. There is such a enormous delight in his face as he encourages Max to make sure to observe all the things that take place in the stars, and report back to him first chance he has.
Lancaster after that point appears periodically throughout the film as we either see Mac reporting him on the sky or Happer is being harassed by a seemingly deranged former employee. Lancaster is rather entertaining in showing the joy in Happer as he seems to absolutely love to hear the various discoveries by Mac as Lancaster gives Happer an endearing childlike enthusiasm. Lancaster contrasts this well with the scenes of Happer being harassed though by showing the complete exasperation at the antics of the man that seemed designed just to get under Happer's skin. Lancaster does this quite well and is particularly funny when he more or less orders for the man to be shot. Lancaster has some excellent comedic timing in these scenes and made me look forward to every time the film cut back to him as he was consistently enjoyable to watch.
Eventually, in the film's climax, Happer comes to Scotland to make a deal with the one holdout on the deal. Happer basically shows up and solves all the problems, and rather quickly wraps up the film. The most important scene in regard to this is actually off screen as it appears that Happer finds a kindred spirit in the one holdout. Lancaster does not get to do a great deal in these scenes, but what does do he does well. He comes in, again with Lancaster's strong presence that he kept while into his later years, and makes Happer's clean up convincing. He also properly calls back to the enthusiasm of his phone calls with Mac to show Happer's change of heart as quite believable showing it to not be much of a change of heart after all. This role is obviously not the biggest challenge of his career, but Lancaster fulfills it wonderfully well proving himself quite capable in a mostly comic role.