  We study the quantum anomalous Hall effect in a strip of stripes model
coupled to a magnetic texture with zero total magnetization and in the presence
of strong electron-electron interactions. A helical magnetization along the
stripes and a spin-selective coupling between the stripes gives rise to a bulk
gap and chiral edge modes. Depending on the ratio between the period of the
magnetic structure and the Fermi wavelength, the system can exhibit the integer
or fractional quantum anomalous Hall effect. In the fractional regime, the
quasiparticles have fractional charges and non-trivial Abelian braid
statistics.
