Drutu–Nowak conjecture on warped cones and coarse Baum–Connes surjectivity

Let $M$ be a compact Riemannian manifold, let $\Gamma\curvearrowright M$ be a measure-preserving action by diffeomorphisms, and let $\mathcal O_\Gamma M$ be the associated warped cone. If the action has a spectral gap, then the coarse assembly map

$$\mu_c\colon KX_*(\mathcal O_\Gamma M)\to K_*(C^*_{\rm Roe}(\mathcal O_\Gamma M))$$

Drutu–Nowak conjecture. The map $\mu_c$ is not surjective for $\mathcal O_\Gamma M$. The conjecture makes precise Roe’s proposed use of warped cones to produce counterexamples to the coarse Baum–Connes conjecture. The supplied text gives no resolution status.