White to move and draw. It is quite long and it requires a lot of calculation and knowledge.
I misplaced the black king. I put it on e3 instead of g3 :(
In any case, to speed things along here is what I was getting at: 1.Rf4! Kg3 2.Rf8 Re4 3.Rh8 h4 4.Rg8 Rg4 5.Rxg4! Kg4 6.Ke1/e2=. The position of the white king is critical in both the drawing lines for white, and those that lose. In the 1.Rb2+ lines, black gets a tempo to push the white king back to the c-file- this is enough to win the game in that line, and 1.Rf4 prevents black from checking from d5 to push the king back to the c-file.
Alena, 4.Ke1 is an illegal move. Is there a typo or an omitted move in your line?
It's a draw.
Now consider this line where black plays to prevent the check from g8 that force the king onto the h-file in front of the pawn: 1.Rf4! Kg3 2.Rf8 Re4 preparing to play Rg4 if needed. How does white deal with this?