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Let   $A$   be a simple separable nuclear C  $^*$  -algebra with a unique tracial state and no unbounded traces, and let   $\alpha $   be a strongly outer action of a finite group   $G$   on   $A$  . In this paper, we show that   $\alpha \otimes \textrm{id}$   on   $A\otimes \mathcal{W}$   has the Rohlin property where   $\mathcal{W}$   is the Razak–Jacelon algebra. Combing this result with the recent classification results and our previous result, we see that such actions are unique up to conjugacy.

Rohlin Actions of Finite Groups on the Razak–Jacelon Algebra