Wooohooooooooo ! Thank you Fencer, this variant rules !
Talking about rules, here are them in short :

A player can capture a piece of his own (except the king), which then becomes part of his stock. When a player has got a piece (or more) in his stock, he can - exactly like in Loop Chess - anytime, in place of a normal move, drop it on any empty square, except the first and last ranks for pawns. One can deliver check or mate in this way.

A king can escape a check by capturing one piece of this own. Unlike Loop Chess, all pieces captured to the opponent are removed from play forever. One cannot capture an own pawn en passant !