An equivariant PPV theorem and Paschke–Higson duality

Abstract

We state the Paschke–Higson duality theorem for a transformation groupoid. Our proof relies on an equivariant localized and norm-controlled version of the Pimsner–Popa–Voiculescu theorem. The main consequence is the existence of a Higson–Roe exact sequence, involving the Baum–Connes assembly map for such a groupoid.