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