  M. Goncharov introduced and studied a Rota--Baxter operator on a
cocommutative Hopf algebra. In the present paper we define relative
Rota--Baxter operators on an arbitrary Hopf algebra. A particular case of this
definition is Goncharov's operator. On a Hopf algebra with a relative
Rota--Baxter operator we define new associative operation and construct a new
Hopf algebra and Hopf brace. Further, we construct Rota--Baxter operators of
integer weights on some groups. The question on a possibility to define
operator of zero weight on groups was formulated by X. Gao, L. Guo, Y. Liu, and
Z.-C. Zhu. In the last section we construct a family of two generated Hopf
algebras. This family includes some known Hopf algebras, in particular,
4-dimensional Sweedler algebra $H_4$.
