The mechanisms of plasma-assisted molecular beam epitaxial growth of GaN on muscovite mica were investigated. Using a battery of techniques, including scanning and transmission electron microscopy, atomic force microscopy, cathodoluminescence, Raman spectroscopy and x-ray diffraction, it was possible to establish that, in spite of the lattice symmetry mismatch, GaN grows in epitaxial relationship with mica, with the [11-20] GaN direction parallel to [010] direction of mica. GaN layers could be easily detached from the substrate via the delamination of the upper layers of the mica itself, discarding the hypothesis of a van der Waals growth mode. Mixture of wurtzite (hexagonal) and zinc blende (ZB) (cubic) crystallographic phases was found in the GaN layers with ratios highly dependent on the growth conditions. Interestingly, almost pure ZB GaN epitaxial layers could be obtained at high growth temperature, suggesting the existence of a specific GaN nucleation mechanism on mica and opening a new way to the growth of the thermodynamically less stable ZB GaN phase.