Theoretical and experimental studies of the B K-shell absorption near the π-excitation in hexagonal boron nitride were carried out. The absorption spectrum over the interval 191.5-193.5 eV was analysed in the framework of the quasi-atomic model with respect to its molecular simulation and for the features of its recombination. Our analysis points to the appearance of local deformations in the crystal lattice around a core-excited atom which are mainly created by the breaking of the ground-state symmetry due to out-of-plane displacements of core-excited boron atoms in a basal plane (0.16 Å). The comparison with the experimental B K-shell absorption spectra for the metastable incoherent phase BN and defect-containing BN crystals supports this polaron mechanism. Methods for the description of the x-ray absorption in solids taking into account the related atomic rearrangement are discussed.