Ideal cotorsion theories in triangulated categories.

We study ideal cotorsion pairs associated to almost exact structures in extension closed subcategories of triangulated categories. This approach allows us to extend the recent ideal approximation theory developed by Fu, Herzog et al. for exact categories in the above mentioned context. In the last part of the paper we apply the theory in order to study projective classes (in particular localization or smashing subcategories) in compactly generated triangulated categories. [ABSTRACT FROM AUTHOR]