  We establish renormalizability of the full spectral action for the Yang-Mills
system on a flat 4-dimensional background manifold. Interpreting the spectral
action as a higher-derivative gauge theory, we find that it behaves
unexpectedly well as far as renormalization is concerned. Namely, a power
counting argument implies that the spectral action is superrenormalizable. From
BRST-invariance of the one-loop effective action, we conclude that it is
actually renormalizable as a gauge theory.
