Cohomological Mackey formula for quotient stacks

In this paper, we construct a restriction morphism on the critical cohomology of an equivariant Landau-Ginzburg model associated to a representation of a reductive group equipped with an invariant function. We show a compatibility formula between the restriction and induction maps as a Mackey-type formula, thereby giving the critical cohomology the structure of a localized induction-restriction system.