  K* mesons and in particular the K*(892) were frequently addressed in lattice
simulations, but always while ignoring that the K*(892) decays strongly. We
present an exploratory extraction of the masses and widths for the K*
resonances by simulating K pi scattering in p-wave with I = 1/2 on the lattice.
The K pi system with total momenta P = 2*pi/L e_z, 2*pi/L (e_x + e_y) and 0,
that allows the extraction of phase shifts at several values of K pi relative
momenta, is studied. A Breit-Wigner fit of the phase renders a K*(892)
resonance mass m^{lat} = 891 +/- 14 MeV and the K*(892) -> K pi coupling
g^{lat} = 5.7 +/- 1.6 compared to the experimental values m^{exp} = 892 MeV and
g^{exp} = 5.72 +/- 0.06, where g parametrizes the K* -> K pi width. When
extracting the phase shift around the K*(1410) and K2*(1430) resonances we take
into account the mixing of p-wave with d-wave and assume that the scattering is
elastic in our simulation. This gives us an estimate of the K*(1410) resonance
mass m^{lat} = 1.33 +/- 0.02 GeV compared to m^{exp} = 1.414 +/- 0.0015 GeV
assuming the experimental K*(1410) -> K pi coupling. We contrast the resonant I
= 1/2 channel with the repulsive non-resonant I = 3/2 channel, where the phase
is found to be negative and small, in agreement with experiment.
