  We consider inclusions of type $(P\otimes A)^G\subset(P\otimes B)^G$, where
$G$ is a compact quantum group of Kac type acting on a ${\rm II}_1$ factor $P$,
and on a Markov inclusion of finite dimensional $C^*$-algebras $A\subset B$. In
the case $[A,B]=0$, which basically covers all known examples, we show that the
planar algebra of such a subfactor is of the form $P(A\subset B)^G$, with $G$
acting in some natural sense on the bipartite graph algebra $P(A\subset B)$.
