Chiral gauge theory and lattice regularization

We discuss for a nonabelian gauge theory with only left handed fields in the continuum the lattice regularization. Global gauge invariance is kept and we argue that if perturbative scaling according to the one loop β-function for a dimensionful and physical quantity is observed the theory behaves as being effectively gauge invariant. Measurable signatures for an intermediate, approximative restoration of local gauge invariance and a problem of the requirement of reflection positivity are discussed. (orig.)