Given a Lie group G and an automorphism σ ∈ G, the twisted loop group Lσ G is the group of continuous paths γ:[0, 1] → G such that γ(1) = σ( γ(0)). Note that if σ is the identity, then Lσ G is the usual (continuous) loop group LG. These groups arise in various places in gauge theory and representation theory.

In this talk, I will explain how to derive formulas for cohomology ring of the classifying space, H*(BLσG) when G is compact and connected, and σ has finite order modulo inner automorphisms. The method of proof can be used more generally to calculate the equivariant cohomology of compact Lie group actions with 'constant rank stabilizers'.