group cohomology, nonabelian group cohomology, Lie group cohomology
Hochschild cohomology, cyclic cohomology?
cohomology with constant coefficients / with a local system of coefficients
differential cohomology
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?
The generalization of the Chern character from K-theory to twisted equivariant K-theory, hence the joint generalization of the twisted Chern character and the equivariant Chern character, typically understood in the context of topological K-theory and then taking values in twisted equivariant de Rham cohomology (including a twist from inner local systems).
Alejandro Adem, Yongbin Ruan, Section 7 of: Twisted Orbifold K-Theory, Commun. Math. Phys. 237 (2003) 533-556 (arXiv:math/0107168)
Varghese Mathai, Danny Stevenson, Chern character in twisted K-theory: equivariant and holomorphic cases, Commun. Math. Phys. 236 (2003) 161-186 (arXiv:hep-th/0201010, doi:10.1007/s00220-003-0807-7)
Jean-Louis Tu, Ping Xu, Chern character for twisted K-theory of orbifolds, Advances in Mathematics Volume 207, Issue 2, 20 December 2006, Pages 455-483 (arXiv:math/0505267, doi:10.1016/j.aim.2005.12.001)
Daniel S. Freed, Michael J. Hopkins, Constantin Teleman, Section 1 of: Twisted equivariant K-theory with complex coefficients 1 1 (2008) 16-44 (arXiv:math/0206257, doi:10.1112/jtopol/jtm001)
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