MIP* Wiki

A positive resolution to Connes' embedding problem would've implied that all countable discrete groups are hyperlinear. Since MIP*=RE gives a negative answer to CEP, this leaves open the possibility that there are non-hyperlinear groups.

One approach to this is to create a linear constraint system (LCS) game $G$ whose commuting operator value $\omega^{co}(G)$ is different from its tensor product value $\omega^*(G)$.