2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63090Motivated 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.17 pages, AMS Latex, uses package DiagramsOperator AlgebrasK-Theory and Homology58B34, 19K33, 46Ltext