For the space of (σ,τ)-derivations of the group algebra C[G] of discrete countable group G, the decomposition theorem for the space of (σ,τ)-derivations, generalising the corresponding theorem on ordinary derivations on group algebras, is established in an algebraic context using groupoids and characters. Several corollaries and examples describing when all (σ,τ)-derivations are inner are obtained. Considered in details cases on (σ,τ)−nilpotent groups and (σ,τ)-FC groups.