Is the crossed product $\mathcal{K} \rtimes G$ a groupoid algebra? Suppose G, a discrete group acting on the compact operators $\mathcal{K}$ by automorphism of C*-algebra $\mathcal{K}$. Can we view the crossed product as a groupoid C*-algebra of some groupoid?
This question occurred to me when I was thinking of possible formulation of Baum-Connes conjecture for projective representation of the group.  
 A: 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.

