  We perform global particle-in-cell simulations of pulsar magnetospheres
including pair production, ion extraction from the surface, frame dragging
corrections, and high energy photon emission and propagation. In the case of
oblique rotators, effects of general relativity increase the fraction of open
field lines which support active pair discharge. We find that the plasma
density and particle energy flux in the pulsar wind are highly non-uniform with
latitude. Significant fraction of the outgoing particle energy flux is carried
by energetic ions, which are extracted from the stellar surface. Their energies
may extend up to a large fraction of the open field line voltage, making them
interesting candidates for ultra-high-energy cosmic rays. We show that pulsar
gamma-ray radiation is dominated by synchrotron emission, produced by particles
that are energized by relativistic magnetic reconnection close to the Y-point
and in the equatorial current sheet. In most cases, calculated light curves
contain two strong peaks, in general agreement with Fermi observations. The
radiative efficiency decreases with increasing pulsar inclination and
increasing efficiency of pair production in the current sheet, explaining the
observed scatter in $L_{\gamma}$ vs $\dot{E}$. We find that the high-frequency
cutoff in the spectra is regulated by the pair loading of the current sheet.
Our findings lay the foundation for quantitative interpretation of Fermi
observations of gamma-ray pulsars.
