The equivariant higher index map is injective for bounded-geometry spaces with properly isometric, bounded-distortion group actions whose quotient and group both coarsely embed into Hilbert space.
Yu, The coarse Baum-Connes conjecture for spaces which admit a u niform embedding into Hilbert space , Invent
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The equivariant coarse Novikov conjecture and coarse embedding
The equivariant higher index map is injective for bounded-geometry spaces with properly isometric, bounded-distortion group actions whose quotient and group both coarsely embed into Hilbert space.