Rokhlin actions and self-absorbing C*-algebras

Let A{script} be a unital separable C*-algebra and D{script} a K1-injective strongly selfabsorbing C*-algebra. We show that if A{script} is D{script}-absorbing, then the crossed product of A{script} by a compact second countable group or by Z{double-struck} or by R{double-struck} is D{script}-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.