On triangulations of orbifolds and formality

For an orbifold, there are two naturally associated differential graded algebras, one is the de Rham algebra of orbifold differential forms and the other one is the differential graded algebra of piecewise polynomial differential forms of a triangulation of the coarse space. In this paper, we prove that these two differential graded algebras are weakly equivalent; hence, the formality of these two differential graded algebras is consistent, when the triangulation is smooth. We show that global quotient orbifolds and global homogeneous isotropy orbifolds admit smooth triangulations; hence, the two kinds of formality coincide with each other for these orbifolds.