  We show that provided $n\ne 3$, the involutive Hopf *-algebra $A_u(n)$
coacting universally on an $n$-dimensional Hilbert space has enough
finite-dimensional representations in the sense that every non-zero element
acts non-trivially in some finite-dimensional *-representation. This implies
that the discrete quantum group with group algebra $A_u(n)$ is maximal almost
periodic (i.e. it embeds in its quantum Bohr compactification), answering a
question posed by P. So tan.
  We also prove analogous results for the involutive Hopf *-algebra $B_u(n)$
coacting universally on an $n$-dimensional Hilbert space equipped with a
non-degenerate bilinear form.
