Tate cohomology for arbitrary groups via satellites (Q1325830)

Tate cohomology, originally defined on finite groups, has been extended to arbitrary groups by Benson and Carlson. The author gives an alternative definition of Benson-Carlson cohomology via satellites; the idea is that Benson-Carlson cohomology is a completion of ordinary cohomology with respect to projective modules. It follows from Mislin's definition that there is a long exact sequence for Benson-Carlson cohomology.