Coarse cone quotients

We study the coarse motive of the quotient ${\mathcal{O}}^{\mathrm{\infty }}(X)\mathrm{/}\mathrm{/}G$ of the cone of a uniform bornological coarse space $X$ with $G$-action. If $X$ admits a sufficiently ergodic probability measure, then we show that the coarse assembly map for ${\mathcal{O}}^{\mathrm{\infty }}(X)\mathrm{/}\mathrm{/}G$ is not an equivalence. The main ideas are taken from a recent paper by C. Kitsios, T. Schick and F. Vigolo (arXiv:2504.21811) and adapted to the formalism of coarse homotopy theory based on bornological coarse spaces developed by A. Engel and the author.