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We describe a construction of cocyclic perturbations of the semigroup ofshifts on the semiaxis by means of the theory of model spaces. It is shown thatone can choose an inner function that determines the model space so that theelements of the perturbed semigroup have a prescribed spectral type and differfrom the elements of the initial semigroup by operators from the Schatten-vonNeumann class $\mathfrak{S}_p$, $p>1$. The case of the trace class$\mathfrak{S}_1$ perturbations is considered separately.

On applications of the model spaces to the construction of cocyclic perturbations of the semigroup of shifts on the semiaxis