In his 2008 paper *Hyperlinear and Sofic Groups: A Brief Guide*, Pestov asked (Open Question 9.5) whether every group with the Haagerup property is hyperlinear (or sofic). Has this question been answered in the meanwhile?

A short recap of the relevant definitions: A group is hyperlinear (sofic) if it embeds into the metric ultraproduct of unitary groups equipped with the normalized Hilbert-Schmidt distance (symmetric groups with the normalized Hamming distance).

A group has the Haagerup property if there is a sequence of positive definite functions that vanish at infinity and converge pointwise to the constant function $1$.