  Intertwining of spin, charge and pairing correlations in the repulsive
two-dimensional Hubbard model is shown through unrestricted variational
calculations, with projected wavefunctions free of symmetry breaking. A
crossover from incommensurate antiferromagnetism to stripe order naturally
emerges in the hole-doped region when increasing the on-site coupling. Although
effective pairing interactions are identified, they are strongly fragmented in
several modes including d-wave pairing and more exotic channels related to an
underlying stripe. We demonstrate that the entanglement of a mean-field
wavefunction by symmetry restoration can largely account for interaction
effects.
