  We construct algebraic cobordism spectra MSL and MSp. They are commutative
monoids in the category of symmetric T^{2}- spectra. The spectrum MSp comes
with a natural symplectic orientation given either by a tautological Thom class
th^{MSp} in MSp^{4,2}(MSp_{2}), a tautological Borel class b_{1}^{MSp} in
MSp^{4,2}(HP^{\infty}) or any of six other equivalent structures. For a
commutative monoid E in the category SH(S) we prove that assignment g ->
g(th^{MSp}) identifies the set of homomorphisms of monoids g : MSp -> E in the
motivic stable homotopy category SH(S) with the set of tautological Thom
elements of symplectic orientations of E. A weaker universality result is
obtained for MSL and special linear orientations.

Algebraic Geometry;K-Theory and Homology