  The effects of electron interaction on the magnetoconductance of graphene
nanoribbons (GNRs) are studied within the Hartree approximation. We find that a
perpendicular magnetic field leads to a suppression instead of an expected
improvement of the quantization. This suppression is traced back to
interaction-induced modifications of the band structure leading to the
formation of compressible strips in the middle of GNRs. It is also shown that
the hard wall confinement combined with electron interaction generates overlaps
between forward and backward propagating states, which may significantly
enhance backscattering in realistic GNRs. The relation to available experiments
is discussed.
