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This paper: http://arxiv.org/abs/1402.3280, says roughly that for every (locally compact Hausdorff) group satisfying the Baum-Connes conjecture with coefficients (e.g. every a-T-menable group), acting on a space, if the associated action groupoid $\Gamma$ carries a $[0,1]$-family of gerbes $\mathcal{G} \to \Gamma\times [0,1]$, then the maps of twisted $C^\ast$-algebras $C^*_r(\Gamma\times[0,1],\omega) \to C^*_r(\Gamma,\omega_t)$ $\forall t\in [0,1]$, induce an isomorphism on K-theory, where $\omega$ is the cocycle classifying the gerbe.
This to me sounds similar to the question in the title of the thread, at least in the special case considered in the paper, which is expected to be true for locally compact groupoids more generally.
Thoughts?
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