For any number h such that hbar:=h/(2\pi) is irrational and any skew-symmetric, non-degenerate bilinear form σ : Z^{2g} × Z^{2g} → Z,, let A_{g,h} the twisted group ∗-algebra C[Z^{2g}] and consider the ergodic group of *-automorphisms of A_{g,h} induced by the action of the symplectic group Sp(Z^{2g},σ) . We show that the only Sp(Z^{2g},σ)-invariant state on A_{g,h} is the trace state.