The equivariant coarse Baum-Connes conjecture for (X, Γ) is equivalent to the groupoid Baum-Connes conjecture for the associated equivariant coarse groupoid G(X, Γ), implying the equivariant coarse Novikov conjecture when X coarsely embeds into Hilbert space.
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A groupoid approach to the equivariant coarse Baum--Connes conjecture
The equivariant coarse Baum-Connes conjecture for (X, Γ) is equivalent to the groupoid Baum-Connes conjecture for the associated equivariant coarse groupoid G(X, Γ), implying the equivariant coarse Novikov conjecture when X coarsely embeds into Hilbert space.