  We consider a modification of QCD in which conventional fundamental quarks
are replaced by Weyl fermions in the adjoint representation of the color SU(N).
In the case of two flavors the low-energy chiral Lagrangian is that of the
Skyrme-Faddeev model. The latter supports topologically stable solitons with
mass scaling as N^2. Topological stability is due to the existence of a
nontrivial Hopf invariant in the Skyrme-Faddeev model. Our task is to identify,
at the level of the fundamental theory, adjoint QCD, an underlying reason
responsible for the stability of the corresponding hadrons. We argue that all
"normal" mesons and baryons, with mass O(N^0), are characterized by (-1)^Q
(-1)^F =1, where Q is a conserved charge corresponding to the unbroken U(1)
surviving in the process of the chiral symmetry breaking (SU(2) \to U(1) for
two adjoint flavors). Moreover, F is the fermion number (defined mod 2 in the
case at hand). We argue that there exist exotic hadrons with mass O(N^2) and
(-1)^Q (-1)^F = -1. They are in one-to-one correspondence with the Hopf
Skyrmions. The transition from nonexotic to exotic hadrons is due to a shift in
F, namely F \to F - {\cal H} where {\cal H} is the Hopf invariant. To detect
this phenomenon we have to extend the Skyrme-Faddeev model by introducing
fermions.
