  This paper is a continuation of the authors article "Enlargements of schemes"
(Log. Anal.1 (2007), no. 1, 1-60) We mainly study the behaviour of etale
cohomology, algebraic cycles and motives under ultraproducts respectively
enlargements. The main motivation for that is to find methods to transfer
statements about etale cohomology and algebraic cycles from characteristic zero
to positive characteristic and vice versa. We give one application to the
independence of $l$ of Betti numbers in etale cohomology and applications to
the complexity of algebraic cycles.
