  Let G be a semisimple Lie group and H a uniform lattice in G. The Selberg
trace formula is an equality arising from computing in two different ways the
traces of convolution operators on the Hilbert space L^2(G/H) associated to
test functions.
  In this paper we present a cohomological interpretation of the trace formula
involving the K-theory of the maximal group C*-algebras of G and H. As an
application, we exploit the role of group C*-algebras as recipients of higher
indices of elliptic differential operators and we obtain the index theoretic
version of the Selberg trace formula developed by Barbasch and Moscovici from
ours.
