Homotopy Representations over the Orbit Category

Abstract

Let G be a finite group. The unit sphere in a finite-dimensional orthogonal G-representation motivates the definition of homotopy representations, due to tom Dieck. We introduce an algebraic analogue, and establish its basic properties including the Borel-Smith conditions and realization by finite G-CW-complexes.

24 pages (revised for improved exposition). To appear in "Homology, Homotopy and Applications". The sequel to this preprint is "Group actions on spheres with rank one isotropy" (arXiv: 1302.0507)