Say that a separable, unital C *-algebra D ≇ C is strongly self-absorbing if there exists an isomorphism ϕ : D → D ⊗ D such that ϕ and id D ⊗ 1 D are approximately unitarily equivalent *-homomorphisms. We study this class of algebras, which includes the Cuntz algebras O 2 , O∞, the UHF algebras of infinite type, the Jiang–Su algebra Z and tensor products of O∞ with UHF algebras of infinite type...