We develop the theory of jitter radiation from GRB shocks containing small-scale magnetic fields and propagating at an angle with respect to the line of sight .
We demonstrate that the spectra vary considerably : the low-energy photon index , \alpha , ranges from 0 to -1 as the apparent viewing angle goes from 0 to \pi / 2 .
Thus , we interpret the hard-to-soft evolution and the correlation of \alpha with the photon flux observed in GRBs as a combined effect of temporal variation of the viewing angle and relativistic aberration of an individual thin , instantaneously illuminated shell .
The model predicts that about a quarter of time-resolved spectra should have hard spectra , violating the synchrotron \alpha = -2 / 3 line of death .
The model also naturally explains why the peak of the distribution of \alpha is at \alpha \approx - 1 .
The presence of a low-energy break in the jitter spectrum at oblique angles also explains the appearance of a soft X-ray component in some GRBs and a relatively small number of them .
We emphasize that our theory is based solely on the first principles and contains no ad hoc ( phenomenological ) assumptions .