A special linear Grassmann variety SGr(k,n) is the complement to the zero
section of the determinant of the tautological vector bundle over Gr(k,n). For
a representable ring cohomology theory A(-) with a special linear orientation
and invertible stable Hopf map \eta, including Witt groups and MSL[\eta^{-1}],
we have A(SGr(2,2n+1))=A(pt)[e]/(e^{2n}), and A(SGr(2,2n)) is a truncated
polynomial algebra in two variables over A(pt). A splitting principle for such
theories is established. We use the computations for the special linear
Grassmann varieties to calculate A(BSL_n) in terms of the homogeneous power
series in certain characteristic classes of the tautological bundle.Comment: Some misprints corrected, slightly revised notatio
