Twisted coarse Novikov conjecture with coefficients

Let $X$ be a metric space with bounded geometry and let $\Gamma(X,\mathcal A)$ be a coarse $X$-algebra. Denote by

$$\mu_{X,\mathcal A}$$

the twisted assembly map associated with $X$ and $\mathcal A$. Twisted coarse Novikov conjecture with coefficients. For every coarse $X$-algebra $\Gamma(X,\mathcal A)$, the twisted assembly map $\mu_{X,\mathcal A}$ is injective. This is the injectivity form of the twisted coarse Baum–Connes assertion; the source introduces it as the coefficient version of the coarse Novikov conjecture, but does not establish it in general.