The Kaon B-parameter in quenched QCD

I report on a recent determination by the ALPHA collaboration of the kaon B-parameter using lattice QCD with Wilson type quarks. An effort is made to control all systematic errors except for the quenched approximation. The preliminary result for the renormalization group invariant parameter is $\hat{B}_K = 0.834(37)$, which translates to $B_K^MSbar(2 GeV)=0.604(27)$ in the MSbar scheme with anticommuting $\gamma_5$.