  We establish a Hirzebruch-Riemann-Roch type theorem and
Grothendieck-Riemann-Roch type theorem for matrix factorizations on quotient
Deligne-Mumford stacks. For this we first construct a
Hochschild-Kostant-Rosenberg type isomorphism explicit enough to yield a
categorical Chern character formula. We next find an expression of the
canonical pairing of Shklyarov under the isomorphism.
