  We describe the structure of the coefficient ring $W^*(pt)=\varOmega_W^*$ of
the $c_1$-spherical bordism theory for an arbitrary $SU$-bilinear
multiplication. We prove that for any $SU$-bilinear multiplication the formal
group of the theory $W^*$ is Landweber exact. Also we show that after inverting
the set $\mathcal P$ of Fermat primes there exists a complex orientation of the
localized theory $W^*[\mathcal P^{-1}]$ such that the coefficients of the
corresponding formal group law generate the whole coefficient ring
$\varOmega_W^*[\mathcal P^{-1}]$.
