Tensor $D$ coaction functors

Abstract

We develop an approach, using what we call "tensor $D$ coaction functors", to the "$C$-crossed-product" functors of Baum, Guentner, and Willett. We prove that the tensor $D$ functors are exact, and identify the minimal such functor. This continues our program of applying coaction functors as a tool in the Baum-Guentner-Willett-Buss-Echterhoff campaign to attempt to "fix" the Baum-Connes conjecture.