  We have surveyed Kepler's supernova remnant in search of the companion star
of the explosion. We have gone as deep as 2.6 solar luminosities in the stars
within 20% of the radius of the remnant. We use FLAMES at the VLT-UT2 telescope
to obtain high resolution spectra of the stellar candidates selected from HST
images. The resulting set of stellar parameters suggests that these stars come
from a rather ordinary mixture of field stars (mostly giants). A few of the
stars seem to have low [Fe/H] (< -1) and they are consistent with being
metal-poor giants. The radial velocities and rotational velocities vrot sin i
are very well determined. There are no fast rotating stars as vrot sin i < 20
km/s. The radial velocities from the spectra and the proper motions determined
from HST images are compatible with those expected from the Besan\c{c}on model
of the Galaxy. The strong limits placed on luminosity suggest that this
supernova could have arisen either from the core-degenerate scenario or from
the double-degenerate scenario.
