Partial tensor-product functors and crossed-product functors

Julian Kranz, Timo Siebenand

Abstract: For a given discrete group G, we apply results of Kirchberg on exact and injective tensor products of $C^*$-algebras to give an explicit description of the minimal exact correspondence crossed-product functor and the maximal injective crossed-product functor for G in the sense of Buss, Echterhoff and Willett. In particular, we show that the former functor dominates the latter.