This puzzle was invented by a guy named Greg who, apparently, invents all sorts of twisty puzzles. It is a harder varient of the master skewb, and contains that puzzles as a factor group. The set of all sequences that preserves the inner core part of the puzzle forms a normal sub-group. Mod-ing out by this sub-group gives us the master skewb.
For this puzzle, I'm going to let W=ULF, X=URF, Y=URB and Z=ULB.
The associated middle layers will be denoted by W', X', Y' and Z', respectively. The corresponding corner twists in the bottom layer will be denoted by w, x, y and z, respectively. (E.g., y=DRB.) The meaning of, say, y' should now be clear. Note that y'=Wi'=W'i.
Solve the inner edges (as apposed to the inner corners) relative to the center dots. Just keep twisting and it practically solves itself.
Align the center window peices with the center dots. Use A=W,Yi,Wi,Y to preserve step 1.
Solve the corner positions. Use Q=3A with setups to do a pair of corner swaps, one in the top layer and one in the bottom.
Orient the corners. Use X,Q,Xi,Q to twist a pair of corners in the top layer. Note that Qi=Q.
Note the obviouse variant Xi,Q,X,Q for twisting in the opposite direction.
This step and step 6 can be done in any order, because here we present a pure tri-cycle of the bars, and in the next step we present a pure tri-cycle of the outer edges peices.
Solve the bars. Use A,y',Ai,y'i. The setups aren't hard.
All that remains now is to position the outer edge peices which are inseparably connected to the inner corners. A pure try-cicle sequence is given by 2[T,Yi,Ti,Y,|2U|] with T=W'i,Y',W',Y'i. Note that we can write T=(Ai')~.
Note that there is a way to use T by itself as a tri-cycle of the edge peices, but you have to apply it and its inverse with appropriate and interleaved setups so that the net number of applications is divisible by 3. An appropriate setup comes from understanding how T alters the inner edge peices. The rotations W and Y are, for example, appropriate setups.