Connes' embedding conjecture for groups

Let $G$ be a countable i.c.c. group, meaning that every conjugacy class other than the identity class is infinite, and let $VN(G)$ be its group von Neumann algebra. Let $R$ be the hyperfinite type $II_1$ factor and let $R^{\omega}$ denote a suitable ultrapower of $R$. Connes' embedding conjecture for groups. For every countable i.c.c. group $G$, the group von Neumann algebra $VN(G)$ embeds into a suitable ultrapower $R^{\omega}$. This is presented as a weaker algebraic version of Connes' embedding conjecture, with the source giving no resolution.