Classification of reduced free products of nuclear C*-algebras

Consider the countably infinite reduced free product $D$ of copies of $(\mathrm C([0,1]),λ)$, where $λ$ is Lebesgue measure. It is proved that finite and countable reduced free products of unital separable nuclear UCT $\mathrm C^*$-algebras with respect to a chosen family of faithful traces are classified, after adjoining $D$, by the Elliott invariant. In other words, an isomorphism between the naive K-theory invariants of two such algebras is induced by an isomorphism between the algebras.