  We summarize recent progress on the symmetric subtraction of the Non-Linear
Sigma Model in $D$ dimensions, based on the validity of a certain Local
Functional Equation (LFE) encoding the invariance of the SU(2) Haar measure
under local left transformations. The deformation of the classical non-linearly
realized symmetry at the quantum level is analyzed by cohomological tools. It
is shown that all the divergences of the one-particle irreducible (1-PI)
amplitudes (both on-shell and off-shell) can be classified according to the
solutions of the LFE. Applications to the non-linearly realized Yang-Mills
theory and to the electroweak theory, which is directly relevant to the
model-independent analysis of LHC data, are briefly addressed.
