Fundamental group of simple $C^{\ast }$-algebras with unique trace II

We show that any countable subgroup of the multiplicative group ${\mathbb{R}}_{+}^{\times }$ of positive real numbers can be realized as the fundamental group $\mathcal{F}(A)$ of a separable simple unital $C^{\ast }$-algebra $A$ with unique trace. Furthermore for any fixed countable subgroup $G$ of ${\mathbb{R}}_{+}^{\times }$, there exist uncountably many mutually nonisomorphic such algebras $A$ with $G=\mathcal{F}(A)$.