  We classify the localizing tensor ideals of the integral stable module
category for any finite group $G$. This results in a generic classification of
$\mathbb{Z}[G]$-lattices of finite and infinite rank and globalizes the modular
case established in celebrated work of Benson, Iyengar, and Krause. Further
consequences include a verification of the generalized telescope conjecture in
this context, a tensor product formula for integral cohomological support, as
well as a generalization of Quillen's stratification theorem for group
cohomology. Our proof makes use of novel descent techniques for stratification
in tensor-triangular geometry that are of independent interest.
