We study Z-actions on unital simple separable stably finite C * -algebras of finite nuclear dimension. Assuming that the extreme boundary of the trace space is compact and finite dimensional, and that the induced action on the trace space is trivial, we show that strongly outer Z-actions have finite Rokhlin dimension in the sense of Hirshberg, Winter and Zacharias.

We study Rokhlin dimension of Z m -actions on simple separable stably finite nuclear C * -algebras. We prove that under suitable assumptions, a strongly outer Z m -action has finite Rokhlin dimension. This extends the known result for automorphisms. As an application, we show that for a large class of C * -algebras, the Z m -Bernoulli action has finite Rokhlin dimension.

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