Given a finite dimensional G-space the mod-p cohomology of the fixed point space can be calculated algebraically by localizing the equivariant cohomology ring. This idea is very fruitful in applications to group actions on spheres. For infinite dimensional spaces fixed points are replaced by homotopy fixed points, and Lannes' T-functor takes the role of localization. I will show that these techniques applied to spherical fibrations over the classifying space BG produce Borel-Smith functions. This relates the study of spherical fibrations over BG to representation theory of G. This work is joint with Ergun Yalcin.