Equivariant coarse Novikov conjecture

Let $X$ be a proper metric space with bounded geometry, and let $\Gamma$ be a countable discrete group acting properly and isometrically on $X$. The equivariant coarse assembly map induced by evaluation is

$$\mu_X^{\Gamma}:\lim_{d\to\infty}K_*(C^*_L(P_d(X))^{\Gamma})\to\lim_{d\to\infty}K_*(C^*(P_d(X)^{\Gamma}))\cong K_*(C^*(X)^{\Gamma}).$$

Equivariant coarse Novikov conjecture. The map $\mu_X^{\Gamma}$ is rationally injective. This is the injectivity part of the equivariant coarse Baum–Connes conjecture and implies the corresponding Novikov-type statement.