right version of the Rokhlin property for actions of finite dimensional quantum groups was given in [@GKL19] under the name “spatial Rokhlin property” and the tracial version of spatial Rokhlin property has not been defined yet. Also, even if we had the result of [@AGP19] for duals of finite dimensional quantum groups, Theorem 4.12 of [@BSV17] would only give the current result assuming approximate representability. It is because of the fact that our actual hypotheses are weaker. Namely, strict approximate innerness is weaker than approximate representability and our results cover also the tracial version of approximate representability.

Finally, in Section \[Sec\_Example\], for every finite group $G$ and for every $\eta \in \left(0, \frac{1}{{{\operatorname{card}}}(G)}\right)$, we construct a simple separable unital AH algebra $A$ with stable rank one and an action $\alpha \colon G \to {{\operatorname{Aut}}}(A)$ such that:

1.  $\alpha$ is pointwise outer, strictly approximately inner, and doesn’t have the weak tracial Rokhlin property.

2.  ${{\operatorname{rc}}}(A) ={{\operatorname{rc}}}\left(C^*(G, A, \alpha)\right)= \eta$.

Acknowledgments {#acknowledgments .unnumbered}
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Some parts of this work were carried out during the research visit of the author to the University of Oregon from March 2018 to September 2019. He is thankful to that institution for its hospitality with special thanks 