I found nice key which works with Opera.
If you press Alt + ~ (Alt and ~) then Opera hides from desktop (not shown in Alt-Tab).
Press Alt+~ one more time and it is back.

Funny thing is that this keys combination works even if Opera is not currently active.
Is it a global hotkey designed to show/hide Opera?

Ctrl+~ is another hotkey which swithes two last tabs no matter how many times you press it - behaviour is different from Ctrl-Tab (I use recently used order option enabled - opera://flags/#activation-order-tab-cycling).

Alt+H also hides Opera but there is no way to unhide it after that.
All this works on Windows XP 64bit.

Are there some other hotkeys?

Thanks