  We investigate the behaviour of tilting sheaves under pushforward by a finite
Galois morphism. We determine conditions under which such a pushforward of a
tilting sheaf is a tilting sheaf. We then produce some examples of Severi
Brauer flag varieties and arithmetic toric varieties in which our method
produces a tilting sheaf, adding to the list of positive results in the
literature. We also produce some counterexamples to show that such a pushfoward
need not be a tilting sheaf.
