Fibrewise stratification of group representations

Given a finite cocommutative Hopf algebra A over a commutative regular ring R, the lattice of localising tensor ideals of the stable category of Gorenstein projective A-modules is described in terms of the corresponding lattices for the fibres of A over the spectrum of R. Under certain natural conditions on the cohomology of A over R, this yields a stratification of the stable category. These results apply when A is the group algebra over R of a finite group, and also when A is the exterior algebra on a finite free R-module.