In this paper, we construct an equivariant coarse homology theory with values in the category of non-commutative motives of Blumberg, Gepner and Tabuada, with coefficients in any small additive category. Equivariant coarse K-theory is obtained from the latter by passing to global sections. The present construction extends joint work of the first named author with Engel, Kasprowski and Winges by promoting the codomain of the equivariant coarse K-homology functor to non-commutative motives.

A great part of this work is a side product of the collaboration with A. Engel, D. Kasprovski, Ch. Winges and M. Ullmann on various projects in equivariant coarse homotopy theory. The authors were supported by the SFB 1085 (DFG).