The Chern–Dold character in cobordisms. I

The fundamental results of the paper are
a) derivation of formulas for the Chern–Dold character $\mathrm{ch}^U$ and $\mathrm{ch}_U$ in the theory of universal bordisms $U_*$ and cobordisms $U^*$, respectively;
b) derivation of the formula of a series over the ring $\Omega^*_u$ which gives addition in the formal group of “geometric” cobordisms, and derivation of the formula for the series $k\Psi^k_U(u)$, where $u\in U^2(CP^\infty_k)$ and the $\Psi^k_U$ are Adams operators in $U^*$-theory.
Bibliography: 12 titles.