Differential forms on orbifolds with corners

Motivated by symplectic geometry, we give a detailed account of differential forms and currents on orbifolds with corners, the pull-back push-forward operations, their fundamental properties. We work within formalism where category corners is obtained as localization etale proper groupoids corners. Constructions proofs are formulated in terms structure maps groupoids, avoiding use orbifold charts. The Frechet space an dual shown to be independent which groupoid chosen represent orbifold.