  We analyze the Swift XRT light curves and spectra of the gamma-ray bursts
(GRBs) for which the redshift has been measured. The sample consists of seven
GRBs. The soft X-ray light curves of all these GRBs are separated into at least
two morphological classes: 1) those starting off with a very steep light curve
decay and 2) those showing a rather mild initial decay. This initial decay is
followed by a flattening and by a further steepening. During these transitions
the soft X-ray spectrum of these GRBs remains constant within the observational
errors (except for one case, GRB050319). For the first time we are able to
exploit the early light curve of GRB afterglows in the comoving frame. Besides
the temporal and spectral behavior we find that the energy of the afterglow
emitted in the (rest frame) time interval 20-200 s and 1300-12600 s after the
trigger correlates with the mean energy of the prompt emission, hinting at a
close link between the two. Averaging over the bursts that have a rather well
sampled light curve and starting immediately after the prompt phase, the energy
emitted in the soft X-rays is about 3% of the energy emitted during the prompt
phase, except for GRB050315, where the soft X-ray emission is as high as 14% of
the prompt emission.
