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It is proved that the K_0-group of a cluster C*-algebra is isomorphic to thecorresponding cluster algebra. As a corollary, one gets a shorter proof of thepositivity conjecture for cluster algebras. As an example, we consider acluster C*-algebra A(1,1) coming from triangulation of an annulus with onemarked point on each boundary component.

K-theory of cluster C*-algebras