Motivic homotopy theory introduced by F. Morel and V. Voevodsky provides a natural setting which allows to apply techniques of algebraic topology to algebraic geometry. One of the first and most striking applications of the theory was Voevodsky's proof of Milnor conjecture, for which he was awarded Fields medal in 2002. Motivic homotopy theory currently is a developing field of mathematics and it continuously incorporates classic topological results and techniques. In particular, one has the following theorems (A. Ananyevskiy). Theorem. Let A(-) be a motivic generalized cohomology theory and let E/X be a vector bundle of odd rank. Suppose that A(P^2)=A(pt). Then A(P(E))=A(pt) and A(P(E+1))=A(pt)+A(pt). As an application of the theorem one can describe the group of stable self-dual vector bundles over projective spaces. This group is an algebraic analogue of the group of stable real vector bundles over real projective spaces in topology (real K-theory of projective spaces). Theorem. Let A(-) be a motivic generalized cohomology theory. Suppose that A(P^2)=A(pt) and A(-) possesses Thom isomorphisms for vector bundles with trivial determinant. Denote X the variety of decomposition of a vector space of dimension 2n into a direct sum of oriented subspaces of dimension two. Then A(X)=A(pt)[e_1,e_2,...,e_n]/(p_1,p_2,...,p_n,s_n), where p_j are elementary symmetric polynomials on the squares of e_i and s_n=e_1e_2...e_n. This theorem yields a theory of Pontryagin classes for SL-oriented motivic generalized cohomology theories and allows to obtain a motivic analogue of Conner-Floyd's theorem relating real K-theory to symplectic cobordism.