  We show that, given a compact Hausdorff space $\Omega$, there is a compact
group ${\mathbb G}$ and a homeomorphic embedding of $\Omega$ into ${\mathbb
G}$, such that the restriction map ${\rm A}({\mathbb G})\to C(\Omega)$ is a
complete quotient map of operator spaces. In particular, this shows that there
exist compact groups which contain infinite cb-Helson subsets, answering a
question raised in [Choi--Samei, Proc. AMS 2013; cf.
http://arxiv.org/abs/1104.2953]. A negative result from the same paper is also
improved.
