Algebraic cobordism and Grothendieck groups over singular schemes (Q2267992)

In 2000, a theorem of \textit{M. Levine} and \textit{F. Morel} [C. R. Acad. Sci., Paris 332, 723--728 (2001; Zbl 0991.19001)] stated that algebraic cobordism groups are isomorphic to (multiplicative) Grothendieck groups over smooth schemes. In this paper the author extended this theorem to singular schemes. As a consequence, the author provides a new proof of the singular Riemann-Roch theorem of Baum-Fulton-MacPherson and a new type of Riemann-Roch theorem with respect to pullbacks of locally complete morphisms.