Local quasiconvexity of groups acting on small cancellation complexes

Given a group acting cellularly and cocompactly on a simply connected 2-complex, we provide a criterion establishing that all finitely generated subgroups have quasiconvex orbits. This work generalizes the “perimeter method”. As an application, we show that high-powered one-relator products A∗B/《rn》 are coherent if A and B are coherent.