  This article provides a geometric bridge between two entirely different
character formulas for reductive Lie groups and answers the question posed by
W.Schmid in [Sch].
  A corresponding problem in the compact group setting was solved by N.Berline,
E.Getzler and M.Vergne in [BGV] by an application of the theory of equivariant
forms and particularly the fixed point integral localization formula. This
article (besides its representation-theoretical significance) provides a whole
family of examples where it is possible to localize integrals to fixed points
with respect to an action of a NONcompact group. Moreover, a localization
argument given here is not specific to the particular setting considered in
this article and can be extended to a more general situation.
  There is a broadly accessible article [L] which explains how the argument
works in the SL(2,R) case, where the key ideas are not obstructed by technical
details and where it becomes clear how it extends to the general case.
