Connes' Embedding Problem and Lance's WEP

Abstract: We will show that a II_1-factor embeds into the ultraproduct of the hyperfinite II_1-factor if and only if it satisfies the von Neumann algebraic analogue of Lance's weak expectation property. This result implies that free group factors (and all other embeddable factors) are built up from the inside (not just in distribution) by the hyperfinite II_1-factor in a way which naturally mixes W* and operator space notions.