  We study the $SU$-linear operations in complex cobordism and prove that they
are generated by the well-known geometric operations $\partial_i$. For the
theory $W$ of $c_1$-spherical bordism, we describe all $SU$-linear
multiplications on $W$ and projections $MU \to W$. We also analyse complex
orientations on $W$ and the corresponding formal group laws $F_W$. The
relationship between the formal group laws $F_W$ and the coefficient ring
$\varOmega^W$ of the $W$-theory was studied by Buchstaber in 1972. We extend
his results by showing that for any $SU$-linear multiplication and orientation
on $W$, the coefficients of the corresponding formal group law $F_W$ do not
generate the ring $\varOmega^W$, unlike the situation with complex bordism.

Algebraic Topology