Borel cohomology and the relative Gorenstein condition for classifying spaces of compact Lie groups.

For a compact Lie group G we show that the representing spectrum for Borel cohomology generates its category of modules if G is connected or if coefficients are of characteristic p and π 0 (G) is a p -group. For a closed subgroup H of G we consider the map C ⁎ (B G) ⟶ C ⁎ (B H) and establish the sense in which it is relatively Gorenstein. Throughout, we pay careful attention to the importance of connectedness of the groups. [ABSTRACT FROM AUTHOR]