2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/70903The fundamental group of a hyperbolic manifold acts on the limit set, giving rise to a cross-product C^* algebra. We construct nontrivial K-cycles for the cross-product algebra, thereby extending some results of Connes and Sullivan to higher dimensions. We also show how the Patterson-Sullivan measure on the limit set can be interpreted as a center-valued KMS state.final versionDifferential GeometryOperator Algebrastext