  We observe that the state space of Landau-Ginzburg isolated singularities is
simply a special case of Chen-Ruan orbifold cohomology relative to the generic
fibre of the potential. This leads to the definition of the cohomology of
hybrid Landau-Ginzburg models and its identification via an explicit
isomorphism to the cohomology of Calabi-Yau complete intersections inside
weighted projective spaces. The combinatorial method used in the case of
hypersurfaces proven by the first named author in collaboration with Ruan is
streamlined and generalised after an orbifold version of the Thom isomorphism
and of the Tate twist.
