Equivariant periodic cyclic homology for ample groupoids

Abstract

We define and study bivariant equivariant periodic cyclic homology for actions of ample groupoids. In analogy to the group case, we show that the theory satisfies homotopy invariance, stability, and excision in both variables. We also prove an analogue of the Green-Julg theorem for actions of proper groupoids.

44 pages. Two errors (in the proof of Theorem 5.8 and Theorem 6.1) fixed, typos corrected