Holmstrom F80 Equivariant cohomology theories

http://www.math.uchicago.edu/~may/BOOKS/alaska.pdf

http://www.math.osu.edu/~joshua.1/bredon_final_aim.pdf

Borel cohomology

Bredon cohomology, presumably also Bredon homology, although the latter may also be some kind of cohomology for (topological???) groups (??).

Chiral equivariant cohomology

Topological Hermitian cobordism

Equivariant algebraic K-theory Equivariant Cech cohomology Equivariant cobordism Equivariant cohomology Equivariant etale cohomology Equivariant higher Chow groups Equivariant homology Equivariant K-theory Equivariant KK-theory Equivariant operational Chow groups Equivariant pretheory Equivariant smooth Deligne cohomology

Generalized Tate cohomology

[arXiv:1207.3459] Permutative G-categories in equivariant infinite loop space theory fra arXiv Front: math.CT av Bertrand Guillou, J. P. May We explain what genuine permutative G-categories are and, more generally, what E infinity G-categories are. We give examples showing how they arise, and we show that they serve as input for an equivariant infinite loop space machine. As a first application, we prove the equivariant Barratt-Priddy-Quillen theorem as a statement about genuine G-spectra and use it to give a new, categorical, proof of the tom Dieck splitting theorem for suspension G-spectra. Other examples are geared towards equivariant algebraic K-theory.

nLab page on F80 Equivariant cohomology theories