Abstract: We show that the classical integral cycle class map from algebraic cycles to étale cohomology factors through a quotient of l-adic étale cobordism over an algebraically closed field of positive characteristic. This implies that there is a strong topological obstruction for cohomology classes to be algebraic and that examples of Atiyah and Hirzebruch for non-algebraic integral cohomology classes and of Totaro for non-trivial elements in the Griffiths group also work in positive characteristic.