EQUIVARIANT KK-THEORY OF r-DISCRETE GROUPOIDS AND INVERSE SEMIGROUPS

摘要

For an r-discrete Hausdorff groupoid g and an inverse semigroup S of slices of g there is an isomorphism between g-equivariant KK-theory and compatible S-equivariant KK-theory. We use it to define descent homomorphisms for S, and indicate a Baum Connes map for inverse semigroups. Also findings by Khoshkam and Skandalis for crossed products by inverse semigroups are reflected in KK-theory.