Title: A universal coarse K-theory,
Abstract: 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 codomain of the equivariant coarse
K-homology functor to non-commutative motives.