Mathematics, Department of


Date of this Version



J. K-Theory 11 (2013), 297–329; doi:10.1017/is013001031jkt214


Copyright © 2013 ISOPP. Used by permission.


We develop a suitable version of the stable module category of a finite group G over an arbitrary commutative ring k. The purpose of the construction is to produce a compactly generated triangulated category whose compact objects are the finitely presented kG-modules. The main idea is to form a localisation of the usual version of the stable module category with respect to the filtered colimits of weakly injective modules. There is also an analogous version of the homotopy category of weakly injective kG-modules and a recollement relating the stable category, the homotopy category, and the derived category of kG-modules.