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.
Dell’Aiera, Controlled K-theory for groupoids & applications to Coarse Geometry, J
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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.