  The polaron, an electron dressed with HCB excitations, remains light even in
the strong coupling limit as its effective mass remains of the order of the
free electron mass. This result is in a sharp contrast to the Holstein model
where the electron effective mass increases exponentially with the
electron-phonon coupling. HCB degrees of freedom mediate the attractive
potential between two electrons that form a bound singlet bipolaron state at
any non-zero coupling strength. In the low-frequency regime of the electron
spectral function we observe a quasi-particle (QP) band that is separated from
the continuum of states only in the central part of the Brillouin zone. The
quasiparticle weight approaches zero as the QP band enters the continuum where
it obtains a finite lifetime. At finite temperature an electron can annihilate
thermally excited HCB's. Such thermally activated processes lead to a buildup
of the spectral weight below the QP band. While the investigated model bears a
resemblance with the Holstein model, we point out many important differences
that originate from the binary HCB excitation spectrum, which in turn mimics
spin-$1\over 2$ degrees of freedom
