  The charge current pumped adiabatically through a deformable quantum dot is
studied within the Green's function approach. Differently from the
non-deformable case, the current shows an undefined parity with respect to the
pumping phase \phi. The unconventional current-phase relation, analyzed in the
weak pumping regime, is due to a dynamical phase shift \phi_D caused by the
elastic deformations of the central region (classical phonons). The role of the
quality factor Q of the oscillator, the effects induced by a mechanical
resonance and the implications for current experiments on molecular systems are
also discussed.
