Equivariant algebraic \(KK\)-theory and adjointness theorems (Q401720)

The article introduces an equivariant version of algebraic \(KK\)-theory for algebras equipped with an action or a grading by a group. Universal properties are discussed. As an algebraic analogue of the Green--Julg Theorem, it is shown that plugging the coefficient ring into the first variable of the equivariant \(KK\)-group yields Weibel's homotopy algebraic \(K\)-theory of the crossed product of the second variable by the group. Furthermore, the induction-restriction adjunction and Baaj--Skandalis Duality are established in this context.