  In this paper we define a Rokhlin property for automorphisms of non-unital
C*-algebras and for endomorphisms. We show that the crossed product of a
C*-algebra by a Rokhlin automorphism preserves absorption of a strongly
self-absorbing C*-algebra, and use this result to deduce that the same result
holds for crossed products by endomorphisms in the sense of Stacey. This
generalizes earlier results of the second named author and W. Winter.
