  Mishchenko-Oliveira proved the piecewise smooth cohomology and Lie algebroid
cohomology of a Lie algebroid on a combinatorial compact manifold are
isomorphic. In this paper, we describe an application of that result locally
trivial Lie groupoids on combinatorial manifolds to obtain an isomorphism
between de Rham cohomology and piecewise de Rham cohomology of left invariants
forms.
