A note on full free product C*-algebras, lifting and quasidiagonality

We study lifting properties for full product C*-algebras with amalgamation over ${\mathbb C}1$ and give new proofs for some results of Kirchberg and Pisier. We extend the result of Choi on the quasidiagonality of $C^*({\mathbb F}_n)$, proving that the free product with amalgamation over ${\mathbb C}1$ of a family of unital quasidiagonal C*-algebras is quasidiagonal.