Related papers: K-theory of certain purely infinite crossed produc…

We show that all amenable, minimal actions of a large class of nonamenable countable groups on compact metric spaces have dynamical comparison. This class includes all nonamenable hyperbolic groups, many HNN-extensions, nonamenable…

We study the C*-algebra crossed product $C_0(X)\rtimes G$ of a locally compact group $G$ acting properly on a locally compact Hausdorff space $X$. Under some mild extra conditions, which are automatic if $G$ is discrete or a Lie group, we…

We study conditions that will ensure that a crossed product of a C*-algebra by a discrete exact group is purely infinite (simple or non-simple). We are particularly interested in the case of a discrete non-amenable exact group acting on a…

We examine crossed product C*-algebras associated with non-minimal free actions of countably infinite discrete abelian groups on the circle, extending the work of Putnam, Schmidt, and Skau. We obtain a large class of unital separable…

Let P be a semigroup that admits an embedding into a group G. Assume that the embedding satisfies a certain Toeplitz condition and that the Baum-Connes conjecture holds for G. We prove a formula describing the K- theory of the reduced…

The $K$-groups of the crossed product of the rotation C*-algebra $A_\theta$ by free and amalgamated products of the cyclic groups $\mathbb Z_n$, for $n=2,3,4,6$, are calculated. The actions here arise from the canonical actions of these…

We introduce the concept of crossed product of a product system by a locally compact group. We prove that the crossed product of a row-finite and faithful product system by an amenable group is also a row-finite and faithful product system.…

We study amenable minimal Cantor systems of free groups arising from the diagonal actions of the boundary actions and certain Cantor systems. It is shown that every virtually free group admits continuously many amenable minimal Cantor…

We unite elements of category theory, K-theory, and geometric group theory, by defining a class of groups called $k$-cube groups, which act freely and transitively on the product of $k$ trees, for arbitrary $k$. The quotient of this action…

We show that several known results about the algebraic K-theory of tensor products of algebras with the C*-algebra of compact operators in Hilbert space remain valid for tensor products with any properly infinite C*-algebra.

Let a compact group G act on real or complex C*-algebras A and B, with A separable and B sigma-unital. We express the G-equivariant Kasparov groups KK_n(A,B) by algebraic K-groups of a certain additive category.

In this paper we analyse for a $G$-$C^{*}$-algebra $A$ to which extent one can calculate the $K$-theory of the reduced crossed product $K(A\rtimes_{r}G)$ from the $K$-theory spectrum $K(A)$ with the induced $G$-action. We also consider some…

I combine recent results in the structure theory of nuclear C*-algebras and in topological dynamics to classify certain types of crossed products in terms of their Elliott invariants. In particular, transformation group C*-algebras…

Building on an argument by Toms and Winter, we show that if $A$ is a simple, separable, unital, $\mathcal{Z}$-stable C*-algebra, then the crossed product of $C(X,A)$ by an automorphism is also Z-stable, provided that the automorphism…

It is shown that if A is an AF algebra then a crossed product of A by the integers can be embedded into an AF algebra if and only if the crossed product is stably finite. This equivalence follows from a simple K-theoretic characterization…

We describe the representation theory of C*-crossed-products of a unital C*-algebra A by the cyclic group of order 2. We prove that there are two main types of irreducible representations for the crossed-product: those whose restriction to…

The multiplicative group of a global field acts on its adele ring by multiplication. We consider the crossed product algebra of the resulting action on the space of Schwartz functions on the adele ring and compute its Hochschild, cyclic and…

Let X be an infinite compact metric space with finite covering dimension and let h be a minimal homeomorphism of X. Let A be the associated crossed product C*-algebra. We show that A has tracial rank zero whenever the image of K_0 (A) in…

Using Kirchberg-Phillips' classification of purely infinite C*-algebras by K-theory, we prove that the isomorphism types of crossed product C*-algebras associated to certain hyperbolic 3-manifold groups acting on their Gromov boundary only…

Let $(\mathcal{A}, G, \alpha)$ be a groupoid dynamical system. We show that if $G$ is assumed to be measurewise amenable and the section algebra $A = \Gamma_0(G^{(0)}, \mathcal{A})$ is nuclear, then the associated groupoid crossed product…