Let 𝒜 be a unital separable
C∗-algebra and 𝒟 a K1-injective strongly self-absorbing 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 satisfies a Rokhlin
property. In the case of a compact Rokhlin action we prove a similar statement about
approximate divisibility.
Keywords
self-absorbing, approximately inner half-flip, crossed
products, Rokhlin property