  Given a group action on a finite set, we define the group-action model which
consists of tensor network diagrams which are invariant under the group
symmetry. In particular, group-action models can be realized as the even part
of group-subgroup subfactor planar algebras. Moreover, all group-subgroup
subfactor planar algebras arise in this way from transitive actions. In this
paper, we provide a universal skein theory for those planar algebras. With the
help of this skein theory, we give a positive answer to a question asked by
Vaughan Jones in the late nineties.
