The $RO(G)$-graded Serre spectral sequence

Abstract

In this paper the Serre spectral sequence of Moerdijk and Svensson is extended from Bredon cohomology to $RO(G)$-graded cohomology for finite groups $G$. Special attention is paid to the case $G= \mathbb{Z}/2$ where the spectral sequence is used to compute the cohomology of certain projective bundles and loop spaces.