I think this is something equivariant
arXiv: Experimental full text search
AT (Algebraic topology)?
Adem-Cohen-Dwyer in CONM96, not so interesting.
[CDATAGreenlees and May: Generalized Tate cohomology (book). This book presents a full and systematic study of a new equivariant cohomology theory t(kG)* constructed from any given equivariant cohomology theory kG, where G is a compact Lie group. The new theories play a central role in relating equivariant algebraic topology with current areas of interest in nonequivariant algebraic topology. Their study is essential to a full understanding of such completion theorems as the Atiyah-Segal completion theorem in K-theory and the Segal conjecture in cohomotopy.]
nLab page on Generalized Tate cohomology