Abstract: Let G act properly and cocompactly by isometries on a CAT(0) space X. A subgroup H is _quasiconvex_ with respect to this action if an orbit Hx in X is quasiconvex. One problem with this notion is that, in general, the quasiconvexity of a subgroup depends on the choice of CAT(0) action.
A CAT(0) 2-complex has _isolated flats_ if its flat planes stay away from each other in a certain precise sense. These complexes with isolated flats share many properties with Gromov's hyperbolic spaces which are not shared by general CAT(0) spaces.
We show that if G acts on a CAT(0) 2-complex with isolated flats, then quasiconvexity is well-defined in the following sense:
Theorem: Let G act properly and cocompactly on a CAT(0) 2-complex X with isolated flats. Suppose that G acts properly and cocompactly on another CAT(0) 2-complex Y. Then a subgroup H is quasiconvex relative to the first action if and only if it is quasiconvex relative to the second action.