  Quillen's algebraic K-theory is reconstructed via Voevodsky's algebraic
cobordism. More precisely, for a ground field k the algebraic cobordism
P^1-spectrum MGL of Voevodsky is considered as a commutative P^1-ring spectrum.
There is a unique ring morphism MGL^{2*,*}(k)--> Z which sends the class
[X]_{MGL} of a smooth projective k-variety X to the Euler characteristic of the
structure sheaf of X. Our main result states that there is a canonical grade
preserving isomorphism of ring cohomology theories MGL^{*,*}(X,U)
\tensor_{MGL^{2*,*}(k)} Z --> K^{TT}_{- *}(X,U) = K'_{- *}(X-U)} on the
category of smooth k-varieties, where K^{TT}_* is Thomason-Trobaugh K-theory
and K'_* is Quillen's K'-theory. In particular, the left hand side is a ring
cohomology theory. Moreover both theories are oriented and the isomorphism
above respects the orientations. The result is an algebraic version of a
theorem due to Conner and Floyd. That theorem reconstructs complex K-theory via
complex cobordism.
