in joint work with Leonardo Patimo, we investigate the compatibility of p-cells with respect to standard parabolic subgroups. Given a p-cell in a standard parabolic subgroup of a crystallographic Coxeter system, one can induce the corresponding cell module and ask whether it decomposes into cell modules. Localization techniques allow us to give an affirmative answer to this question. Along the way, we prove some new positivity properties of the p-canonical basis.