Loop groups and twisted K-theory I

Understand

This is the first in a series of papers investigating the relationship between the twisted equivariant K-theory of a compact Lie group G and the "Verlinde ring" of its loop group.

• In this paper we set up the foundations of twisted equivariant K-groups, and more generally twisted K-theory of groupoids.
• We establish enough basic properties to make effective computations.
• Using the Mayer-Vietoris spectral sequence we compute the twisted equivariant K-groups of a compact connected Lie group G with torsion free fundamental group.