  The evolution kernels that govern the scale dependence of the generalized
parton distributions are invariant under transformations of the
$\mathrm{SL}(2,\mathrm R)$ collinear subgroup of the conformal group. Beyond
one loop the symmetry generators, due to quantum effects, differ from the
canonical ones. We construct the transformation which brings the {\it full}
symmetry generators back to their canonical form and show that the eigenvalues
(anomalous dimensions) of the new, canonically invariant, evolution kernel
coincide with the so-called parity respecting anomalous dimensions. We develop
an efficient method that allows one to restore an invariant kernel from the
corresponding anomalous dimensions. As an example, the explicit expressions for
NNLO invariant kernels for the twist two flavor-nonsinglet operators in QCD and
for the planar part of the universal anomalous dimension in $ N=4$ SYM are
presented.
