I have a problem with threads in my JSF application, maybe somebody could help me.
After the start I run new thread which is making some background
Maybe you can solve your problem with asynchronous background work with ICEfaces server side push.
Pleas take a look at http://auctionmonitor.icefaces.org/auctionMonitor/auctionMonitor.jsf for an example of the push technology.
Your background working thread could perform a "push", which will "notify" certain pages to update (partially) and display your message.