Bredon cohomology

Summary

Bredon cohomology is a cohomology theory for spaces with an action of a group $G$. Its coefficients are not one group but a system of groups, one for each orbit type $G/H$. It is computed from the cell structure of a $G$-CW complex and keeps track of the fixed point sets $X^H$ of all subgroups $H$. It is the basic ordinary cohomology theory of equivariant homotopy theory, and the obstructions of equivariant obstruction theory lie in it.