Vagabond Chess

The board is 8x8, but consists of 4 different 4x4 quadrants. A double line shows where the quadrant ends.

Pieces move as they do in orthodox chess, but it's also possible to move to the corresponding square in another quadrant.

Setup

Starting position:
R	E	E	K	A	A	V	R
P	P	P	P	P	P	P	P
							
							
							
							
P	P	P	P	P	P	P	P
R	E	E	K	A	A	V	R

Pieces

A=Archbishop (knight + bishop compound)

E=Berserker  The Berserker can move as a knight does, and can also take out any agent the same way a knight could take out an enemy agent. The berserker is always able to take out friendly agents, but is not allowed to take out the friendly king. The berserker does not give check to the friendly king, even when a knight's move away or similar.

Additionally to the knight’s way of moving, a berserker can jump any given agent in all orthogonal jumping directions, given that it is orthogonally adjacent to the berserker right before the move is made. The berserker will then end up on the other side of the jumped agent (orthogonally adjacent, but on the other side). Any agents (friends or enemies) located in the 2 squares that are a knight’s move away, in the same direction the jump was made, from the jumped agent fall victims to the rage of the berserker and is removed from the board.  That goes whether they are friend or foe, and it is not optional. The jumped agent is unaffected. If the friendly king is in "capturing position" (a knight's move away from the jumped agent, in the jumping direction), then the berserker jump is not allowed.

V=Vagabond   Vagabonds move and take out enemy agents like a knight does when they're located on the rim of a quadrant. When they're on the centermost 4 squares of any quadrant they're able to move as a queen, but then they can't take out any agents. 

When vagabonds are on the outermost rim of the 8x8 board they're additionally able to move, but not capture enemies, diagonally backwards out of the board, and will thus materialize on the opposite side of the 8x8 board. A vagabond on b1 could move to a8 or c8, but can't take out enemies on any of those squares. A vagabond on a1 could move to h2, b8, or h8, but can't take out enemies on any of those squares. 

Vagabonds are worldly enough that they won't give check to the enemy king, but they're not above capturing other agents. So kings are safe, friendly agents are safe, but no other enemy agents are safe from the vagabond.

Rules

Change of rules from orthodox chess:
¤ The board is divided into 4 quadrants. All pieces and pawns, but not the kings, may move to any of the corresponding squares in the other 3 quadrants, but only as long as it’s an unoccupied square, and it doesn’t result in either check or mate. For instance, the square b2 corresponds to squares b6, f2, and f6 – since they’re located in corresponding places within the four quadrants. The 8x8 board works the same as in orthodox chess, so it’s entirely possible to move the ordinary way, crossing the border of the quadrant.
¤ Castling is free.
¤ Pawns don’t promote, and neither does any other agent. 
¤ Pawns are berolina plus pawns. They're always able to move 2 square ahead diagonally when they're on the player's second rank.
¤ Vagabonds move like knights along the rims of the quadrants, and they move like queens on the centermost 4 squares of every quadrant. They can not take out agents when moving as queens. The “backwards diagonal” move typical of vagabonds only work across the entire 8x8 board (and from along the rim of the board itself), and not across only the quadrant.
¤ Kings will only work as kings usually do, so there’s no change about
the kings from how they work in orthodox chess. They can't move to another
quadrant the way it would have worked in orthodox chess, but they can't
jump to the corresponding square in another quadrant.