  The Jones polynomial and Khovanov homology of a classical link are invariants
that depend upon an initial choice of orientation for the link. In this paper,
we give a Khovanov homology theory for unoriented virtual links. The graded
Euler characteristic of this homology is proportional to a similarly-defined
unoriented Jones polynomial for virtual links, which is a new invariant in the
category of non-classical virtual links. The unoriented Jones polynomial
continues to satisfy an important property of the usual one: for classical or
even virtual links, the unoriented Jones polynomial evaluated at one is two to
the power of the number of components of the link. As part of extending the
main results of this paper to non-classical virtual links, a new framework for
computing integral Khovanov homology is described that can be efficiently and
effectively implemented on a computer. We define an unoriented Lee homology
theory for virtual links based upon the unoriented version of Khovanov
homology.
