I need additional clarification.
If I got correctly from this link Where Federation authentication token is saved [WIF STS]? and other general WIF-STS discussions, STS token is in default scenario stored in cookie in an browser. In my browser it is split in two cookies started with FedAuth. It is OK. If I understood good, cookie is created by WIF after STS token validation on RolePlayer application. If it is like that, then cookie is in RolePlayer application domain. When user hit RolePlayer2 application (that is in federation and in second domain) then how STS knows about that user, when it has not access to created cookie.
Could you clarify this to me please ?