Symmetric Operations

The aim of the article is to construct certain natural cohomological operations acting in the ring of algebraic cobordisms of smooth projective varieties. The Chow traces of these operations coincide with the halves of the Chow traces of certain Landweber–Novikov operations. These operations are used to construct nontrivial maps between Chow rings of different varieties. This technique is applied to the computation of discrete invariants of quadrics.