  Given a polynomial $W$ with an isolated singularity, we can consider the
Jacobian ring as an invariant of the singularity. If in addition we have a
group action on the polynomial ring with $W$ fixed, we are led to consider the
twisted Jacobian ring which reflects the equivariant structure as well. Our
main result is to show that the twisted Jacobian ring is isomorphic to an
endomorphism ring of the "twisted diagonal" matrix factorization. As an
application, we suggest a way to investigate Floer theory of Lagrangian
submanifolds which represent homological mirror functors.
