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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.
For a discrete group $G$, we develop a `$G$-balanced tensor product of two coactions $(A,delta)$ and $(B,epsilon)$, which takes place on a certain subalgebra of the maximal tensor product $Aotimes_{max} B$. Our motivation for this is that we are able
In further study of the application of crossed-product functors to the Baum-Connes Conjecture, Buss, Echterhoff, and Willett introduced various other properties that crossed-product functors may have. Here we introduce and study analogues of these pr
A cosystem consists of a possibly nonselfadoint operator algebra equipped with a coaction by a discrete group. We introduce the concept of C*-envelope for a cosystem; roughly speaking, this is the smallest C*-algebraic cosystem that contains an equiv
Canonical tensor product subfactors (CTPSs) describe, among other things, the embedding of chiral observables in two-dimensional conformal quantum field theories. A new class of CTPSs is constructed some of which are associated with certain modular i
We show that Kraus property $S_{sigma}$ is preserved under taking weak* closed sums with masa-bimodules of finite width, and establish an intersection formula for weak* closed spans of tensor products, one of whose terms is a masa-bimodule of finite