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What does the Serre functor of equivariant category of fractional CY category look like?

I am considering the following set up. Let $\mathcal{A}$ be a fractional Calabi-Yau category and denote by $S$ the Serre functor and $S^m=[n]$. Now I consider a finite group action $G$ on $\mathcal{A}$...
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