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Have you seen Packeryou seen Packer-Raeburn Stabilization tricktrick? ( Transactions of the AMS 334(2), p. 685-718, 1992).

Judith A. Packer and Iain Raeburn, On the structure of twisted group $C^*$-algebras, Trans. Amer. Math. Soc. 334 no 2 (1992), 685-718, doi:10.1090/S0002-9947-1992-1078249-7

Specially theorem 3Theorem 3.4 therein stablishes that the algebra is morita equivalent to a Twisted Group C*-therein establishes that the algebra is Morita equivalent to a Twisted Group $C^*$-algebra, summarizing the answer bythe answer by N. Ozawa and the correctionOzawa and the correction above.

By considering the trick of viewing the algebra considering the trick of viewing the algebra $K\rtimes G$ as a locally trivialas a locally trivial bundle with a $G$-action over a contractibleover a contractible $G$- spacespace $X$ ( For instancefor instance, the total space of the universal the total space of the universal $G$-Bundle $EG$, but also the spacebut also the space $\underline{E}G$ worksworks), you cancan see thethe $C*$ algebra in question$C^*$-algebra in question is morita equivalent to the algebr aMorita equivalent to the algebra of sections of the Fell bundle over the transformationsections of the Fell bundle over the transformation groupoid $X\rtimes G$. THis has ben documented inThis has been documented in Kumjian's monograph http://www.theta.ro/jot/archive/1988-020-002/1988-020-002-002.pdfmonograph

Alex Kumjian, On equivariant sheaf cohomology and elementary $C^*$-bundles, J. Operator Theory 20 (1988), no. 2, 207–240 (journal pdf)

Other references onreferences on this kind of trickskind of tricks include http://jlms.oxfordjournals.org/content/50/1/170.abstract ,

Siegfried Echterhoff, Morita Equivalent Twisted Actions and a New Version of the Packer-Raeburn Stabilization Trick, Journal of the London Mathematical Society 50 Issue 1 (1994) 170–186, doi:10.1112/jlms/50.1.170

and partpart 5 here: https://arxiv.org/abs/1501.06050

Noé Bárcenas, Twisted geometric K-homology for proper actions of discrete groups, Journal of Topology and Analysis (2018) doi:10.1142/S1793525319500729, arXiv:1501.06050.

Have you seen Packer-Raeburn Stabilization trick? ( Transactions of the AMS 334(2), p. 685-718, 1992). Specially theorem 3.4 therein stablishes that the algebra is morita equivalent to a Twisted Group C*- algebra, summarizing the answer by N. Ozawa and the correction above.

By considering the trick of viewing the algebra $K\rtimes G$ as a locally trivial bundle with a $G$-action over a contractible $G$- space $X$ ( For instance, the total space of the universal $G$-Bundle $EG$, but also the space $\underline{E}G$ works), you can see the $C*$ algebra in question is morita equivalent to the algebr a of sections of the Fell bundle over the transformation groupoid $X\rtimes G$. THis has ben documented in Kumjian's monograph http://www.theta.ro/jot/archive/1988-020-002/1988-020-002-002.pdf

Other references on this kind of tricks include http://jlms.oxfordjournals.org/content/50/1/170.abstract , and part 5 here: https://arxiv.org/abs/1501.06050

Have you seen Packer-Raeburn Stabilization trick?

Judith A. Packer and Iain Raeburn, On the structure of twisted group $C^*$-algebras, Trans. Amer. Math. Soc. 334 no 2 (1992), 685-718, doi:10.1090/S0002-9947-1992-1078249-7

Specially Theorem 3.4 therein establishes that the algebra is Morita equivalent to a Twisted Group $C^*$-algebra, summarizing the answer by N. Ozawa and the correction above.

By considering the trick of viewing the algebra $K\rtimes G$ as a locally trivial bundle with a $G$-action over a contractible $G$-space $X$ (for instance, the total space of the universal $G$-Bundle $EG$, but also the space $\underline{E}G$ works), you can see the $C^*$-algebra in question is Morita equivalent to the algebra of sections of the Fell bundle over the transformation groupoid $X\rtimes G$. This has been documented in Kumjian's monograph

Alex Kumjian, On equivariant sheaf cohomology and elementary $C^*$-bundles, J. Operator Theory 20 (1988), no. 2, 207–240 (journal pdf)

Other references on this kind of tricks include

Siegfried Echterhoff, Morita Equivalent Twisted Actions and a New Version of the Packer-Raeburn Stabilization Trick, Journal of the London Mathematical Society 50 Issue 1 (1994) 170–186, doi:10.1112/jlms/50.1.170

and part 5 here:

Noé Bárcenas, Twisted geometric K-homology for proper actions of discrete groups, Journal of Topology and Analysis (2018) doi:10.1142/S1793525319500729, arXiv:1501.06050.