Stratifying the derived category of cochains on BG for G a compact Lie group

The main purpose of this paper is to classify the localising subcategories of the derived category where G is a compact Lie group and k is a field. We also prove a version of Chouinard’s theorem for , we describe the relationship between induction and coinduction for a closed subgroup of G, and we use this to describe the relationship between Hochschild homology and cohomology of C∗(BG;k).