Complex cobordism MU${}^{\ast }[1\mathrm{/}2]$ modulo MSU${}^{\ast }[1\mathrm{/}2]$ and related genera

This paper presents a commutative complex oriented cohomology theory with coefficients the quotient ring of complex cobordism MU${}^{\ast }[1\mathrm{/}2]$ modulo the ideal generated by any subsequence of any polynomial generators in special unitary cobordism MSU${}^{\ast }[1\mathrm{/}2]$ viewed as elements in MU${}^{\ast }[1\mathrm{/}2]$ by forgetful map.