Tensorially absorbing inclusions of C*-algebras

When D is strongly self-absorbing, we say an inclusion B ⊆ A of C*-algebras is D -stable if it is isomorphic to the inclusion B ⊗ D ⊆ A ⊗ D . We give ultrapower characterizations and show that if a unital inclusion is D -stable, then D -stability can be exhibited for countably many intermediate C*-algebras concurrently. We show that such unital embeddings between unital D -stable C*-algebras are point-norm dense in the set of all unital embeddings, and that every unital embedding between D -stable C*-algebras is approximately unitarily equivalent to a D -stable embedding. Examples are provided.