Sentence:  Indeed, by a profound result of E. Kirchberg, F. Radulescu and N. Ozawa, a group is <WSD>hyperlinear</WSD> if and only if it satisfies the Connes embedding conjecture for groups, that is, if and only if its von Neumann algebra embeds into an ultrapower of the hyperfinite II<sub>1</sub> factor R. 
Meaning of the word marked with <WSD> tags:  Displaying a generalization of sofic that applies to finite-dimensional Hilbert spaces.