  Let $P \subset A$ be a inclusion of unital C*-algebras and $E\colon A \to P$
be a conditional expectation of index finite type. We introduce a Rokhlin
property for $E$ and discuss about $\mathcal{D}$-absorbing proeprty, where
$\mathcal{D}$ is a separable, unital, strongly self-absorbing C*-algebra. In
this paper we consider permanent properties for strongly self-absorbing
property under inclusions of unital C*-algebras with a finite Watatani index.
