  We give a detailed proof of a new characterization of the Weak Expectation
Property (WEP) announced by Haagerup in the 1990's but unavailable (in any
form) till now. Our main result is motivated by a well known conjecture of
Kirchberg, which is equivalent to the Connes embedding problem. We review the
basic relevant facts connecting our main theorem with the latter conjecture,
along the lines of our forthcoming lecture notes volume on the Connes-Kirchberg
problem.
