In this talk we will discuss the application of the technique developed by Calmes-Petrov Zainoulline to oriented cohomology of algebraic groups and motives of twisted flag varieties. In particular we will show how one can compare oriented cohomology of algebraic group to its chow ring. As an example, we will be able to compute algebraic cobordism of some groups of small ranks. Also we will discuss the relation between the Chow motive of a twisted flag variety and its h-motive for an oriented cohomology h.