Made in China, 2010.
(plastic, 2.6" square, white opposite yellow, blue opposite green, orange opposite red;
Crazy Cube 2x3x3 and Crazy Cube 3x3x3 are smaller versions;
Crazy Cube 4x4x4 Two has a larger center circle)

Faces rotate around the center circle; here is a sequence of three face rotations:



Here is a sequence of 4 rotations about the center:



Jaap's Page presents a solution.

Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/crazy444.htm