Quasi-regular representations of discrete groups and associated C*-algebras

We introduce several equivalence relations on the set of subgroups of a countable group G, defined in terms of the quasi-regular representations, and present some rigidity results in terms of these equivalence relations for certain classes of subgroups. Furthermore, we present some results concerning the ideal structure of the C*-algebras generated by the quasi-regular representations.
This is joint work with Bachir Bekka.