On the lifting property for $C^$-algebras

We characterize the lifting property (LP) of a separable C^* -algebra A by a property of its maximal tensor product with other C^* -algebras, namely we prove that A has the LP if and only if for any family \{D_i\mid i\in I\} of C^* -algebras the canonical map {\ell_\infty(\{D_i\}) \otimes_{\max} A}\to {\ell_\infty(\{D_i \otimes_{\max} A\}) } is isometric. Equivalently, this holds if and only if M \otimes_{\max} A= M \otimes_\mathrm{nor} A for any von Neumann algebra M .