  We introduce the concept of nested topological order in a class of exact
quantum lattice Hamiltonian models with non-abelian discrete gauge symmetry.
The topological order present in the models can be partially destroyed by
introducing a gauge symmetry reduction mechanism. When symmetry is reduced in
several islands only, this imposes boundary conditions to the rest of the
system giving rise to topological ground state degeneracy. This degeneracy is
related to the existence of topological fluxes in between islands or,
alternatively, hidden charges at islands. Additionally, island deformations
give rise to an extension of topological quantum computation beyond
quasiparticles.

Strongly Correlated Electrons;High Energy Physics - Theory;Quantum Physics