  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.
