It is known that oriented cohomology of algebraic varieties generalizes the notion of the Chow group and the Grothendieck group, and each oriented cohomology determines a formal group law. On the other hand, the classical characteristic map provides a combinatorial tool to study the Chow group (and the Grothendieck group) of complete flags. In this talk I will introduce the formal group algebras and the characteristic maps introduced by Calmes-Petrov-Zainoulline. Then I will talk about applying it to study the gamma filtration of oriented cohomology of complete flags. This is joint work with J. Malagon-Lopez and K. Zainoulline.