Integral motivic sheaves and geometric representation theory

With representation-theoretic applications in mind, we con-struct a formalism of reduced motives with integral coef-ficients. These are motivic sheaves from which the higher motivic cohomology of the base scheme has been removed. We show that reduced stratified Tate motives satisfy favor-able properties including weight and t-structures. We also prove that reduced motives on cellular (ind-)schemes unify various approaches to mixed sheaves in representation the-ory, such as Soergel-Wendt's semisimplified Hodge motives, Achar-Riche's complexes of parity sheaves, as well as Ho-Li's recent category of graded 8-adic sheaves.(c) 2022 Elsevier Inc. All rights reserved