Ozawa's nuclear embedding conjecture for exact C*-algebras

Let $\mathcal{A}$ be an exact C*-algebra, meaning that its reduced C*-algebra is exact. Let $I(\mathcal{A})$ denote the injective envelope of $\mathcal{A}$. Ozawa's conjecture. There is a nuclear C*-algebra $N(\mathcal{A})$ such that

$$\mathcal{A} \subset N(\mathcal{A}) \subset I(\mathcal{A}).$$

Ozawa proved this construction for reduced C*-algebras of free groups, while the conjecture asks for it for every exact C*-algebra. In the paper, the authors prove the conjecture for reduced C*-algebras of discrete groups by identifying exactness with amenability of the action on the Furstenberg boundary.