  This paper is a contribution to the general program introduced by Isaacs,
Malle and Navarro to prove the McKay conjecture in the representation theory of
finite groups. We develop new methods for dealing with simple groups of Lie
type in the defining characteristic case. Using a general argument based on the
representation theory of connected reductive groups with disconnected center,
we show that the inductive McKay condition holds if the Schur multiplier of the
simple group has order 2. As a consequence, the simple groups \Orth_{2m+1}(p^n)
and PSp_{2m}(p^n) are "good" for p>2 and the simple groups E_7(p^n) are
``good'' for p>3 in the sense of Isaacs, Malle and Navarro. We also describe
the action of the diagonal and field automorphisms on the semisimple and the
regular characters.
