Precomputed radiance transfer (PRT) captures realistic lighting effects from distant, low-frequency environmental lighting but has been limited to static models or precomputed sequences. We focus on PRT for local effects such as bumps, wrinkles, or other detailed features, but extend it to arbitrarily deformable models. Our approach applies zonal harmonics (ZH) which approximate spherical functions as sums of circularly symmetric Legendre polynomials around different axes. By spatially varying both the axes and coefficients of these basis functions, we can fit to spatially varying transfer signals. Compared to the spherical harmonic (SH) basis, the ZH basis yields a more compact approximation. More important, it can be trivially rotated whereas SH rotation is expensive and unsuited for dense per-vertex or per-pixel evaluation. This property allows, for the first time, PRT to be mapped onto deforming models which re-orient the local coordinate frame. We generate ZH transfer models by fitting to PRT signals simulated on meshes or simple parametric models for thin membranes and wrinkles. We show how shading with ZH transfer can be significantly accelerated by specializing to a given lighting environment. Finally, we demonstrate real-time rendering results with soft shadows, inter-reflections, and subsurface scatter on deforming models.