Analytic equivariant coarse Novikov conjecture

Let $\Gamma$ be a countable discrete group, and let $X$ be a proper metric space with a free and proper $\Gamma$-action. Consider the map

$$\nu_X^{\Gamma}:\lim_{d,n\to\infty}K_*^{\Gamma}(\widetilde{P_{d,n}}(X))\otimes\mathbb Q\xrightarrow{\pi_*}\lim_{d\to\infty}K_*^{\Gamma}(P_d(X))\otimes\mathbb Q\to K_*(C^*(X)^{\Gamma})\otimes\mathbb Q.$$

Analytic equivariant coarse Novikov conjecture. The composition of $\pi_*$ and the assembly map, namely the Miščenko–Kasparov assembly map $\nu_X^{\Gamma}$, is injective. This is a rational injectivity statement for the analytic assembly map in the presence of a free and proper group action.