  We propose a nonlocal definition of a gauge-invariant object in terms of the
Wilson loop operator in a non--Abelian gauge theory. The trajectory is a closed
curve defined by an (untraced) Wilson loop which takes its value in the center
of the color group. We show that definition shares basic features with the
gauge-dependent 't Hooft construction of Abelian monopoles in Yang-Mills
theories. The chromoelectric components of the gluon field have a hedgehog-like
behavior in the vicinity of the object. This feature is dual to the structure
of the 't Hooft-Polyakov monopoles which possesses a hedgehog in the magnetic
sector. A relation to color confinement and lattice implementation of the
proposed construction are discussed.
