Purely infinite, simple $C^{*}$-algebras arising from free product constructions. III

In the reduced free product of C$^{*}$-algebras, $(A,\phi )=(A_{1},\phi _{1})*(A_{2},\phi _{2})$ with respect to faithful states $\phi _{1}$ and $\phi _{2}$, $A$ is purely infinite and simple if $A_{1}$ is a reduced crossed product $B\rtimes _{\alpha ,r}G$ for $G$ an infinite group, if $\phi _{1}$ is well behaved with respect to this crossed product decomposition, if $A_{2}\ne \mathbf{C}$ and if $\phi$ is not a trace.