Particle-in-Cell (PIC) simulations of relativistic shear boundary layers show that strong organized magnetic fields and nonthermal particles are created by collisionless plasma processes. In many cases the nonthermal particles form a power-law spectrum truncated at low energies depending on the shear Lorentz factor. We present synchrotron and SSC spectra computed from first principles radiated by such shear boundary layers, and compare them with GRB spectra observed by Fermi and other satellites. The spectral parameters extracted from such spectral fits will be confronted with GRB jet models.