The motivic Chern class is a K-theoretic generalization of the MacPherson class in homology. In this talk, I will discuss some properties of the motivic Chern classes of the Schubert cells in the flag varieties, and their applications in the representation theory of the p-adic Langlands dual group and the Lenart-Zainoulline-Zhong conjecture about the Schubert classes in the hyperbolic cohomology theory of the flag varieties. Based on several joint works with Aluffi, Lenart, Mihalcea, Naruse, Schurmann, Zainoulline, and Zhong.