Traces on Noncommutative Homogeneous Spaces

We study properties of C*-algebraic deformations of homogeneous spaces G/Γ which are equivariant in the sense that they preserve the natural action of G by left translation. The center is shown to be isomorphic to C(G/G0ρ) for a certain subgroup G0ρ of G, and there is a 1–1 correspondence between normalised traces and probability measures on G/G0ρ. This makes it possible to represent the deformed algebra as operators over L2(G/Γ). Applications to K-theory are also mentioned.