Equivariant Z-stability for single automorphisms on simple C∗-algebras with tractable trace simplices

Let A be an algebraically simple, separable, nuclear, Z -stable C ∗ -algebra for which the trace space T ( A ) is a Bauer simplex and the extremal boundary ∂ e T ( A ) has finite covering dimension. We prove that each automorphism α on A is cocycle conjugate to its tensor product with the trivial automorphism on the Jiang–Su algebra. At least for single automorphisms this generalizes a recent result by Gardella–Hirshberg–Vaccaro. If α is strongly outer as an action of Z , we prove it has finite Rokhlin dimension with commuting towers. As a consequence it tensorially absorbs any automorphism on the Jiang–Su algebra.