Related papers: Exotic crossed products and the Baum-Connes conjec…
For an $r$-discrete Hausdorff groupoid ${\cal G}$ and an inverse semigroup $S$ of slices of ${\cal G}$ there is an isomorphism between ${\cal G}$-equivariant $KK$-theory and compatible $S$-equivariant $KK$-theory. We use it to define…
We study the Farrell-Jones Conjecture with coefficients in an additive G-category with involution. This is a variant of the L-theoretic Farrell-Jones Conjecture which originally deals with group rings with the standard involution. We show…
Every hyperbolic group acts continuously on its Gromov boundary. One can form the corresponding cross-product C*-algebra A. We show that there always exists a canonical Poincare duality map from the K-theory of A to the K-homology of A. We…
We study the K-theory of the Cuntz-Nica-Pimsner C*-algebra of a rank-two product system that is an extension determined by an invariant ideal of the coefficient algebra. We use a construction of Deaconu and Fletcher that describes the…
In this paper, we use the KK-theory of Kasparov to prove exactness of sequences relating the K-theory of a real C^*-algebra and of its complexification (generalizing results of Boersema). We use this to relate the real version of the…
We study a Going-Down (or restriction) principle for ample groupoids and its applications. The Going-Down principle for locally compact groups was developed by Chabert, Echterhoff and Oyono-Oyono and allows to study certain functors, that…
We prove the Baum--Connes conjecture with arbitrary coefficients for some classes of groups: (1) Linear algebraic groups over a non-archimedean local field. (2) Linear algebraic groups over the adeles of a global field k, provided that at…
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 $A\otimes_{\max} B$. Our motivation for this is…
We establish a connection between Cohen-Lyndon triples and equivariant homology theory, with a focus on the Baum-Connes conjecture. In the first part of this work, we establish an excision sequence for the classifying spaces for proper…
We formulate a version of Baum-Connes' conjecture for a discrete quantum group, building on our earlier work (\cite{GK}). Given such a quantum group $\cla$, we construct a directed family $\{\cle_F \}$ of $C^*$-algebras ($F$ varying over…
We show that a $KK$-equivalence between two unital $C^*$-algebras produces a correspondence between their DG categories of finitely generated projective modules which is a $\mathbf{K}_*$-equivalence, where $\mathbf{K}_*$ is Waldhausen's…
The external Kasparov product is used to construct odd and even spectral triples on crossed products of $C^*$-algebras by actions of discrete groups which are equicontinuous in a natural sense. When the group in question is $\Z$ this gives…
It is shown that a C*-algebra generated by any faithful covariant representation of a Hilbert bimodule X is canonically isomorphic to the crossed product associated to X provided that Rieffel's induced representation functor X-ind is…
The equivariant coarse index is well-understood and widely used for actions by discrete groups. We extend the definition of this index to general locally compact groups. We use a suitable notion of admissible modules over $C^*$-algebras of…
We use a recent result by Cuntz, Echterhoff and Li about the K-theory of certain reduced C*-crossed products to describe the K-theory of C*_r(S) when S is an inverse semigroup satisfying certain requirements. A result of Milan and Steinberg…
Franke's reconstruction functor R is known to provide examples of triangulated equivalences between homotopy categories of stable model categories, which are exotic in the sense that the underlying model categories are not Quillen…
Let G be a locally compact group and rho a non-unitary finite dimensional representation of G. We consider tensor products of rho by some unitary representations of G in order to define two Banach algebras analogous to the group…
For a countable discrete group $G$, we construct a new and concrete model for the equivariant topological $K$-homology theory of $G$, which is defined for all $G$-actions, not just for proper $G$-actions. The construction of our model…
We study index pairings for crossed-product $C^*$-algebras arising from minimal actions on the Cantor set. We utilize Putnam's orbit-breaking AF-subalgebras and embeddings to show we can compute any index pairing for Cantor minimal system…
In this paper, we introduce a notion of twisted Roe algebra and a twisted coarse Baum-Connes conjecture with coefficients. We will study the basic properties of twisted Roe algebras, including a coarse analogue of the imprimitivity theorem…