An entry in the 19th fortnightly challenge...
Above is a 9x9 "chess" board with some pieces already laid out, your goal is to fill the board completely, following standard Sudoku rules (i.e. every cell should be filled, such that a specific piece of a given colour appears only once per row, column and 3x3 block). The only additional rule being that black kings may not be in check by any white pieces (in the finished grid). This "check" rule applies across region boundaries (for example, you can't put a black king on the bottom row of the top left 3x3 because of the white queen in the row below).
The nine unique pieces that you need to fit to the grid are:
Finally, note that I've added the no-computers tag. It's not a particularly brutal Sudoku, so you shouldn't need any solvers to help you.
Credits: component images come from lichess, though I believe they just use freely available images anyway.
Answer
If I didn't make any mistakes, this should do:
Insights into the solving process:
The first thing I noticed was that no white queen and black king could be adjacent. This observation is enough to place every white queen and black king on the board.
With every black king on the board, the location for the other white pieces is considerably restricted: I started by placing a few white knights, because their checks can't be obstructed, followed by a few white rooks. At this point it can be solved almost like a normal sudoku; because I'm not very well versed on how to do this properly, I had to use the Poor Man's Sudoku Solver:
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