A universal coarse K-theory

TL;DR

This paper develops a universal equivariant coarse K-theory framework using non-commutative motives, extending previous work by broadening the codomain to include non-commutative motives with coefficients in any small additive category.

Contribution

It introduces a new equivariant coarse homology theory valued in non-commutative motives, generalizing prior constructions and enhancing the scope of equivariant coarse K-theory.

Findings

Constructed an equivariant coarse homology theory with non-commutative motives.

Extended previous work by promoting the codomain to non-commutative motives.

Provides a universal framework for equivariant 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.