  In this paper we verify Navarro's refinement of the McKay conjecture for
quasi-simple groups of Lie type in their defining characteristic. Navarro's
refinement takes into account the action of specific Galois automorphisms on
the characters present in the McKay conjecture. Our proof of this case of the
conjecture relies on a character correspondence constructed by Maslowski.
Building on this we verify the inductive condition for Navarro's refinement for
most groups of Lie type in defining characteristic.
