  Solitons of a nonlinear field interacting with fermions often acquire a
fermionic number or an electric charge if fermions carry a charge. We show how
the same mechanism (chiral anomaly) gives solitons statistical and rotational
properties of fermions. These properties are encoded in a geometrical phase,
i.e., an imaginary part of a Euclidian action for a nonlinear sigma-model. In
the most interesting cases the geometrical phase is non-perturbative and has a
form of an integer-valued theta-term.
