Hall-effect thrusters, which are electrostatic devices based on an E B ´ plasma discharge, have successfully been used as satellite propulsion systems for the last few decades. However, the presence of anomalous electron cross-field transport is still poorly understood, and involves complex and strongly coupled mechanisms such as azimuthal electron drift instabilities and intense secondary electron emission (SEE) from the thruster walls. The present work focuses on the relative importance of these two phenomena. We use a 2D particle-in-cell/Monte Carlo collision model configured to simulate the radial-azimuthal directions near the thruster exit plane. A constant radial magnetic field and axial electric field are imposed, and electron drift instabilities are observed in the azimuthal (E B ´) direction. A simplified SEE model is implemented and an extensive parametric study is performed to directly determine the effect on electron transport. It is found that, for the operating conditions used in our simulations, SEE enhances the near-wall electron mobility by a factor 2, while reducing the bulk plasma mobility by about 20% (due to electron cooling). However, the dominant contribution to anomalous electron transport is still observed to be caused by electron drift instabilities driven by the E B ´ discharge configuration. SEE modifies the electron mobility profile, but the spatially-averaged value remains relatively constant. Three different operating regimes are identified depending on the SEE rate value: two that are stable, and a third which shows an oscillatory behaviour. In addition to electron transport, the kinetic simulations give new insight into the plasma sheath formation at the radial walls, and comparison with typical analytical sheath models demonstrate important differences.