Abstract
In this article we prove that the additive invariant corepresented by the noncommutative motive $\mathbb{Z}[r]$ is the Grothendieck group of endomorphisms functor $K_0\mathrm{End}$. Making use of Almkvist’s foundational work, we then show that the ring $\mathrm{Nat}(K_0\mathrm{End},K_0\mathrm{End})$ of natural transformations (whose multiplication is given by composition) is naturally isomorphic to the direct sum of $\mathbb{Z}$ with the ring $W_0(\mathbb{Z}[r])$ of fractions of polynomials with coefficients in $\mathbb{Z}[r]$ and constant term 1.
Citation
Goncalo Tabuada. "Co-representability of the Grothendieck group of endomorphisms functor in the category of noncommutative motives." Homology Homotopy Appl. 13 (2) 315 - 328, 2011.
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