We study the classifying space of a twisted loop group , where is a compact Lie group and is an automorphism of of finite order modulo inner automorphisms. Equivalently, we study the –twisted adjoint action of on itself. We derive a formula for the cohomology ring and explicitly carry out the calculation for all automorphisms of simple Lie groups. More generally, we derive a formula for the equivariant cohomology of compact Lie group actions with constant rank stabilizers.
"Classifying spaces of twisted loop groups." Algebr. Geom. Topol. 16 (1) 211 - 229, 2016. https://doi.org/10.2140/agt.2016.16.211