  We present the solution of the one-dimensional t-V model with twisted
boundary conditions in the strong coupling limit, t<<V and show that this model
can be mapped onto the strong coupling Hubbard chain threaded by a fictitious
flux proportional to the total momentum of the charge carriers. The high energy
eigenstates are characterized by a factorization of degrees of freedom
associated with configurations of soliton and antisoliton domains and degrees
of freedom associated with the movement of ``holes'' through these domains. The
coexistence of solitons and antisolitons leads to a strange flux dependence of
the eigenvalues. We illustrate the use of this solution, deriving the full
frequency dependence of the optical conductivity at half-filling and zero
temperature.
