  It is shown that the basic observed properties of the gamma-ray bursts (GRBs)
are accounted for if one assumes that the GRBs arise by blueshifting the
emission radiation of hydrogen and helium generated during the last scattering
epoch. The blueshift generator for a single GRB is a region with a nonconstant
bang-time function $t_B(r)$ (described by a Lema\^{\i}tre -- Tolman (L--T)
exact solution of Einstein's equations) matched into a homogeneous and
isotropic (Friedmann) background. Blueshift visible to the present observer
arises \textit{only on those rays that are emitted radially in an L--T region}.
The paper presents three L--T models with different Big Bang profiles, adapted
for the highest and the lowest end of the GRB frequency range. The models
account for: (1) The observed frequency range of the GRBs; (2) Their limited
duration; (3) The afterglows; (4) Their hypothetical collimation into narrow
jets; (5) The large distances to their sources; (6) The multitude of the
observed GRBs. Properties (2), (3) and (6) are accounted for only
qualitatively. With a small correction of the parameters of the model, the
implied perturbations of the CMB radiation will be consistent with those
actually caused by the GRBs. A complete model of the Universe would consist of
many L--T regions with different $t_B(r)$ profiles, matched into the same
Friedmann background. This paper is meant to be an initial exploration of the
possibilities offered by models of this kind; the actual fitting of all
parameters to observational results requires fine-tuning of several
interconnected variables and is left for a separate study.
