  We analyze the Chern-Simons-like term generation in the CPT-odd
Lorentz-violating Yang-Mills theory interacting with fermions. Moreover, we
study the anomalies of this model as well as its quantum stability. The whole
analysis is performed within the algebraic renormalization theory, which is
independent of the renormalization scheme. In addition, all results are valid
to all orders in perturbation theory. We find that the Chern-Simons-like term
is not generated by radiative corrections, just like its Abelian version.
Additionally, the model is also free of gauge anomalies and quantum stable.
