  We prove a criterion of when a coaction of a compact Lie group on an algebra
of continuous functions on a compact manifold extends to a coaction of
deformation quantizations of the Lie group and the algebra. We compute an
explicit example of a compact quantum group $SU(3)_\theta$, which arises as a
deformation quantization of the Lie group $SU(3)$ by an action of its maximal
torus. Using the criterion, we determine exactly when the action of $SU(3)$ on
$S^5$ extends to a coaction of $SU(3)_\theta$ on the noncommutative 5-sphere
$S^5_{\theta'}$. Furthermore, this coaction is shown to be cotransitive. A
coaction of $SU(3)_\theta$ on the product of two noncommutative 5-sphere
$(S^5\times S^5)_{\theta'}$ with nontrivial algebra of coinvariant elements is
given and associated projective modules are constructed.
