  We study the pointed or copointed liftings of Nichols algebras associated to
affine racks and constant cocycles for any finite group admitting a principal
YD-realization of these racks. In the copointed case we complete the
classification for the six affine racks whose Nichols algebra is known to be of
finite dimension. In the pointed case our method allows us to finish four of
them. In all of the cases the Hopf algebras obtained turn out to be cocycle
deformations of their associated graded Hopf algebras. All of them are new
examples of finite-dimensional copointed or pointed Hopf algebras over
non-abelian groups.
