We define``tracial''analogs of the Rokhlin property for actions of finite groups, approximate
representability of actions of finite abelian groups, and approximate innerness. We prove the …

Let A be a separable, unital, simple, Z-stable, nuclear C⁎-algebra, and let α: G→ Aut (A) be
an action of a discrete, countable, amenable group. Suppose that the orbits of the action of G …

We consider a certain class of unital simple stably finite C*-algebras which absorb the Jiang-
Su algebra Z tensorially. Under a mild assumption, we show that the crossed product of a C …

Noncommutative geometry studies an interplay between spatial forms and algebras with
non-commutative multiplication. This book covers the key concepts of noncommutative …

Let P be a semigroup that admits an embedding into a group G. Assume that the embedding
satisfies the Toeplitz condition recently introduced by the third named author and that the …

We prove that a number of classes of separable unital C*-algebras are closed under
crossed products by finite group actions with the Rokhlin property, including:(a) AI algebras …

Let A be an algebraically simple, separable, nuclear, Z-stable C∗-algebra for which the
trace space T (A) is a Bauer simplex and the extremal boundary∂ e T (A) has finite covering …

We describe some of the forms of freeness of group actions on noncommutative C*-algebras
that have been used, with emphasis on actions of finite groups. We give some indications of …

We compute the K-theory of C*-algebras generated by the left regular representation of left
Ore semigroups satisfying certain regularity conditions. Our result describes the K-theory of …

This book grew out of the Oberwolfach Seminar “K-Theory for Group C∗-Algebras and
Semigroup C∗-Algebras” organized by the authors in October 2014. In this seminar, we …