  In this paper we prove two formulas for the characters of representations of
reductive groups. Both express the character of a representation in terms of
the same geometric data attached to it. When specialized to the case of a
compact Lie group, one of them reduces to Kirillov's character formula in the
compact case, and the other, to an application of the Atiyah-Bott fixed point
formula to the Borel-Weil realization of the representation.
