The state space of the \(K_ 0\)-group of a simple separable \(C^*\)- algebra (Q1342767)

Let \(A\) be an unital \(C^*\)-algebra, \(SK_0 (A)= \{\sigma\in \Hom (K_0 (A), \mathbb{R})\): \(\sigma (K_0 (A)^+ )\subseteq \mathbb{R}^+\), \(\sigma[ 1]= 1\}\) be the state space of \(K_0 (A)\). The purpose of this paper is to improve this situation by constructing a separable, simple, unital \(C^*\)-algebra \(A\) such that \(SK_0 (A)\) is affinely homeomorphic to an arbitrary given metrizable compact convex set.