geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Orbifold differential K-theory is a generalization of differential K-theory from smooth manifolds to orbifolds, hence enhancement of orbifold K-theory to differential cohomology. On global quotient orbifolds this is typically supposed to reduce to equivariant differential K-theory.
Richard Szabo, Alessandro Valentino, Ramond-Ramond Fields, Fractional Branes and Orbifold Differential K-Theory, Commun. Math. Phys. 294:647-702, 2010 (arXiv:0710.2773)
Ulrich Bunke, Thomas Schick, Differential orbifold K-Theory, J. Noncommut. Geom. 7 4 (2013) 1027-1104 [arXiv:0905.4181, ems:3926]
Ulrich Bunke, Thomas Schick, Section 9 of: Differential K-theory. A survey, Global differential geometry, Springer, Heidelberg (2012), 303-358 (arXiv:1011.6663, doi:10.1088/1126-6708/1998/12/019)
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