Algebras with grading by a discrete can be deformed using 2-cocycles on the base group. We give a K-theoretic isomorphism of such deformations, generalizing the previously known cases of the theta-deformations and the reduced twisted group algebras. When we perturb the deformation parameter, the monodromy of the Gauss-Manin connection on the cyclic cohomology of deformed algebras can be identified with the action of the exponential of the 2-cocycle in the group cohomology.