Non-perturbative renormalization in kaon decays

We discuss the application of the MPSTV non-perturbative method [1] to the operators relevant to kaon decays. This enables us to reappraise the long-standing question of the ΔI = 12 rule, which involves power-divergent subtractions that cannot be evaluated in perturbation theory. We also study the mixing with dimension-six operators and discuss its implications to the chiral behaviour of the BK parameter.