Rational equivalence of 0-cycles on $K3$ surfaces and conjectures of Huybrechts and O'Grady

We give a new interpretation of O’Grady’s filtration on the $C{H}_0$ group of a $K3$ surface. In particular, we get a new characterization of the canonical 0-cycles $k{c}_X$ : this is the only 0-cycle on $X$ whose orbit under rational equivalence is of dimension $k$. Using this, we extend results of Huybrechts and O’Grady concerning Chern classes of simple vector bundles on $K3$ surfaces.