Torus-equivariant homological mirror symmetry for toric Fano stacks

Let $\Delta$ be a convex lattice polytope in $\bR^n$ containing the origin in its interior. Let $X$ be the associated toric Fano stack, let $\bT$ be the $n$-dimensional torus acting on $X$, and let $\Wtilde$ be the pullback of a Laurent polynomial mirror $W$ to the universal cover $\bC^n$ of $(\bC^*)^n$. Write $D^b \operatorname{Coh}^{\bT}(X)$ for the derived category of $\bT$-equivariant coherent sheaves. Torus-equivariant homological mirror symmetry conjecture. There is an equivalence of triangulated categories

$$D^b \operatorname{Coh}^{\bT}(X) \cong D^b \Fuk \Wtilde.$$

This equivariant refinement implies ordinary homological mirror symmetry for $X$ and for finite torus quotient stacks. The paper proves it when $X$ is projective space, but the assertion for general convex lattice polytopes remains open in the source.