Twisted equivariant K-theory, groupoids and proper actions

Abstract

In this paper we define twisted equivariant K-theory for actions of Lie groupoids. For a Bredon-compatible Lie groupoid, this defines a periodic cohomology theory on the category of finite CW-complexes with equivariant stable projective bundles. A classification of these bundles is shown. We also obtain a completion theorem and apply these results to proper actions of groups.

26 pages

References in corpus (4)

• Twisted K-theory and loop group representations
• Homotopy Theory of Orbispaces
• Equivariant representable K-theory
• The Atiyah--Segal completion theorem in twisted K-theory

Cited by in corpus (2)

• Proper actions and decompositions in equivariant K-theory
• The Completion Theorem in twisted equivariant $K$-Theory for proper and discrete actions