  By adding or removing appropriate structures to Gauss diagram, one can create
useful objects related to virtual links. In this paper few objects of this kind
are studied: twisted virtual links generalizing virtual links; signed chord
diagrams staying halfway between twisted virtual links and Kauffman bracket /
Khovanov homology; alternatable virtual links intermediate between virtual and
classical links. The most profound role here belongs to a structure that we
dare to call orientation of chord diagram. Khovanov homology is generalized to
oriented signed chord diagrams and links in oriented thickened surface such
that the link projection realizes the first Stiefel-Whitney class of the
surface. After this paper was published, V.O.Manturov succeeded in extending
Khovanov homology with arbitrary coefficients to arbitrary virtual links, see
arXiv: math.GT/0601152.
