In this talk, I will explain our work on $G$-twisted version of  pre-calculi structures on Hochschild chains of a certain type of curved algebras.  We have studied a large class of LG orbifolds and their formal Frobenius manifolds via the deformation theory, which are conjectured to be equivalent to those of their mirror orbifold LG A-models. As an application, I will show the calculation for ADE singularities on orbifolds. This is a joint work with Weiqiang He and Si Li.