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A Decomposition of Twisted Equivariant $K$-Theory
Symmetry, integrability and geometry: methods and applications, Tome 17 (2021) Cet article a éte moissonné depuis la source Math-Net.Ru

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For $G$ a finite group, a normalized $2$-cocycle $\alpha\in Z^{2}\big(G,{\mathbb S}^{1}\big)$ and $X$ a $G$-space on which a normal subgroup $A$ acts trivially, we show that the $\alpha$-twisted $G$-equivariant $K$-theory of $X$ decomposes as a direct sum of twisted equivariant $K$-theories of $X$ parametrized by the orbits of an action of $G$ on the set of irreducible $\alpha$-projective representations of $A$. This generalizes the decomposition obtained in [Gómez J.M., Uribe B., Internat. J. Math. 28 (2017), 1750016, 23 pages, arXiv:1604.01656] for equivariant $K$-theory. We also explore some examples of this decomposition for the particular case of the dihedral groups $D_{2n}$ with $n\ge 2$ an even integer.
Keywords: twisted equivariant $K$-theory, $K$-theory, finite groups. 
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     author = {Jos\'e Manuel G\'omez and Johana Ram{\'\i}rez},
     title = {A {Decomposition} of {Twisted} {Equivariant} $K${-Theory}},
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     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a40/}
}
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José Manuel Gómez; Johana Ramírez. A Decomposition of Twisted Equivariant $K$-Theory. Symmetry, integrability and geometry: methods and applications, Tome 17 (2021). http://geodesic.mathdoc.fr/item/SIGMA_2021_17_a40/

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