Monoidal model structures over infinite groups

The stable category of modules over the algebra of a finite group with coefficients in a field is a compactly generated tensor triangulated category, that has been studied extensively in representation theory. In this paper, we provide a plethora of infinite groups G, for which the category of kG-modules (where k is a commutative coherent ring of finite global dimension) admits a monoidal model structure, in the sense of Hovey, whose associated homotopy category is a compactly generated tensor triangulated category. To that end, we use a technique recently introduced by the authors, which is based on Kropholler's operation LH and the second author's operation Φ.