  The 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.

Differential Geometry;Operator Algebras