Equivariant split generation and mirror symmetry of special isogenous tori

We prove a version of equivariant split generation of Fukaya category when a symplectic manifold admits a free action of a finite group G. Combining this with some generalizations of Seidel's algebraic frameworks from [35], we obtain new cases of homological mirror symmetry for some symplectic tori with non-split symplectic forms, which we call special isogenous tori. This extends the work of Abouzaid-Smith [2]. We also show that derived Fukaya categories are complete invariants of special isogenous tori.