Let A be a unital separable C∗-algebra, and D a K1-injective strongly selfabsorbing C∗-algebra. We show that if A is D-absorbing, then the crossed product of A by a compact second countable group or by Z or by R is D-absorbing as well, assuming the action satisfying a Rokhlin property. In the case of a compact Rokhlin action we prove a similar statement about approximate divisibility.

Let G be an inductive limit of finite cyclic groups and let A be a unital simple projectionless C∗-algebra with K1(A) = G and with a unique tracial state, as constructed based on dimension drop algebras by Jiang and Su. First, we show that any two aperiodic elements in Aut(A)/WInn(A) are conjugate, where WInn(A) means the subgroup of Aut(A) consisting of automorphisms which are inner in the tra...

We introduce and study the continuous Rokhlin property for actions of compact groups on C*-algebras. An important technical result is a characterization in terms asymptotic retracts. As consequence, we derive strong KK-theoretical obstructions to property. Using these, show that UCT preserved under formation crossed products passage fixed point algebras by such actions, even absence nuclearity....

We prove that the notion of rigidity (or relative property (T)) for inclusions of finite von Neumann algebras defined in [Po1] is equivalent to a weaker property, in which no “continuity constants” are required. The notion of relative property (T) (or rigidity) for inclusions of finite von Neumann algebras with countable decomposable center was introduced in ([P1]) by requiring that one of the ...

Let G be a countable abelian group. We construct a unital simple projectionless C∗-algebra A with a unique tracial state, that satisfies (K0(A), [1A]) ∼= (Z, 1), K1(A) ∼= G, A ⊗ Z ∼= A, and that is obtained as the inductive limit C∗-algebra of a sequence of dimension drop algebras of a specific form. This construction is based on the construction of the Jiang-Su algebra. By this construction, w...