K-homology of certain group C*-algebras

Abstract

Motivated by the search for new examples of ``noncommutative manifolds'', we study the noncommutative geometry (in the sense of Connes) of the group C*-algebras of various discrete groups. The examples we consider are the infinite dihedral group Z \times_σ $Z_2$ and the semidirect product group $Z \times_σ Z$. We present a unified treatment of the K-homology and cyclic cohomology of these algebras.