Title: Stable and Unstable Operations in mod p Cohomology Theories
Authors: Andrew Stacey and Sarah Whitehouse
Author's e-mail address: a.e.stacey@sheffield.ac.uk s.whitehouse@sheffield.ac.uk
AMS classification number: 55S25, 55P47
Other useful information: math.AT/0605471
Abstract: 
We consider operations between two multiplicative, complex orientable
cohomology theories. Under suitable hypotheses, we construct a map
from unstable to stable operations, left-inverse to the usual map from
stable to unstable operations.  In the main example, where the target
theory is one of the Morava K-theories, this provides a simple and
explicit description of a splitting arising from the Bousfield-Kuhn
functor.

This is an updated version of an earlier submission.  The proof of
proposition 3.2 has been corrected; other minor improvements have been made.