Notes on twisted equivariant K-theory for C*-algebras

摘要

In this paper, we study a generalization of twisted (groupoid) equivariant K-theory in the sense of Freed-Moore for Z(2)-graded C*-algebras. It is defined by using Fredholm operators on Hilbert modules with twisted representations. We compare it with another description using odd symmetries, which is a generalization of van Daele's K-theory for Z(2)-graded Banach algebras. In particular, we obtain a simple presentation of the twisted equivariant K-group when the C*-algebra is trivially graded. It is applied for the bulk-edge correspondence of topological insulators with CT-type symmetries.