The basic and most fundamental computation for an oriented cohomology theory is thE projective bundle theorem claiming A(P^n_k) to be a truncated polynomial ring over A(k) with an explicit basis given by the powers of a Chern class. Having this result at hand one can introduce characteristic classes and carry out a variety of <<geometric>> computations. We establish analogous results for a representable SL-oriented cohomology theory A_\eta with the stable Hopf map inverted. A typical example of a cohomology theory with the prescribed properties is given by the derived Witt groups with the special linear orientation defined via Koszul complexes. It turns out that in this setting one should look at the varieties SL_{n+2}/(SL_2x SL_n) instead of the projective spaces P^n.