T-duality in an H-flux: Exchange of Momentum and Winding

Using our earlier proposal for Ramond-Ramond fields in an H-flux on loop space [13], we extend the Hori isomorphism in [6, 7] from invariant differential forms, to invariant exotic differential forms such that themomentum and winding numbers are exchanged, filling in a gap in the literature. We also extend the compatibility of the action of invariant exact Courant algebroids on the T-duality isomorphism in [10], to the T-duality isomorphism on exotic invariant differential forms.