A construction of universal dynamical ℛ-matrices is presented. It is based on a solution ℱ of a shifted cocycle relation. ℱ provides a twist from the usual universal ℛ-matrix to a dynamical one, solution of the Gervais-Neveu-Felder equation. In the second part, we construct two quantum spin chain Hamiltonians with quantum sl(2|1) invariance. These spin chains define variants of the Hubbard model and describe electron models with pair hoppings.