A K-theoretic Selberg trace formula.

Abstract

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 operators on the Hilbert space L^2(G/H) associated to compactly supported smooth functions on G. Barbasch and Moscovici used the Selberg trace formula to compute multiplicities of unitary representations of G in L^2(G/H), by introducing an index theory interpretation of the trace formula. \nIn this paper we take their index theoretic interpretation further and obtain a K-theoretic interpretation of the trace formula. This relies on a commuting diagram which displays a relationship between K-theory of the maximal group C*-algebra of G and that of H.