We construct differential K-theory of representable smooth orbifolds as a ring valued functor with the usual properties of a differential extension of a cohomology theory. For proper submersions (with smooth fibres) we construct a push-forward map in differential orbifold K-theory. Finally, we construct a non-degenerate intersection pairing with values in for the subclass of smooth orbifolds which can be written as global quotients by a finite group action. We construct a real subfunctor of our theory, where the pairing restricts to a non-degenerate -valued pairing.
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Ulrich Bunke, Thomas Schick, Differential orbifold K-theory. J. Noncommut. Geom. 7 (2013), no. 4, pp. 1027–1104DOI 10.4171/JNCG/143