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
Be?linson-Bernstein localization?
Equivariant differential K-theory is an equivariant cohomology-enhancement of differential K-theory, or conversely a differential cohomology-enhancement of equivariant K-theory.
This is supposed to coincide with orbifold differential K-theory on global quotient orbifolds.
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 (2013), no. 4, 1027-1104 (arXiv:0905.4181)
Michael L. Ortiz, Differential Equivariant K-Theory (arXiv:0905.0476)
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)