Bounded Novikov conjecture for foliations

Let $(M,\mathcal{F})$ be a foliation on a compact manifold, let $BG$ be the classifying space of its holonomy groupoid, and let $\mathcal{L}^{lf}$ be the cosheaf assigning to each $x\in BG$ the locally finite $L$-homology of the leaf through $x$. Let $L_*^{\mathcal{F},bdd}(M)$ denote the bounded foliated surgery group. Bounded Novikov conjecture for foliations. If the leaves of $(M,\mathcal{F})$ are uniformly contractible, then the map

$$H_*(BG;\mathcal{L}^{lf})\to L_*^{\mathcal{F},bdd}(M)$$

is injective. This is a foliated analogue of the Novikov conjecture, asserting injectivity of the bounded surgery assembly map under a uniform contractibility hypothesis on the leaves.