  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_{\sigma} $Z_2$ and the semidirect product
group $Z \times_{\sigma} Z$. We present a unified treatment of the K-homology
and cyclic cohomology of these algebras.
