Can a spinning object stop spinning? Suppose there's an object spinning in empty space. That object has mass and angular momentum. Is it possible for that object to stop spinning without any external intervention, say due to a chemical reaction that transforms its "global" angular momentum into lots of little cases of "local" angular momentum, whereby the microscopic constituents of the object begin spinning so as to "absorb" the global angular momentum of the object?
 A: Internal constituents can affect the angular velocity of the system. Here is an example. So the answer is yes. If you are in a space probe spinning along some axis, then turning on a tape recoder or an HDD aligned with the axis can slow down the spin of the space probe. The total angular momentum is still conserved. 
A: You can use energy to create opposing angular momentum - BUT the created AM becomes an energy store and must be maintained to maintain the cancellation of external rotation. An example is a "momentum wheel"* which is a wheel which rotates in the plane of rotation of the satellite and which can be spun up to impart rotation in one direction and spun down or reversed in direction to alter rotation in the other direction. A limitation is that the wheel will reach some maximum rated speed if always accelerated in the same direction and must them be maintained at that speed if the losses in speed are not to impart rotation to the overall system.
*The term "reaction wheel" is also used. Some sources use the terms interchangeably while others may use "reaction wheel" for change in angular momentum and momentum wheel for devices mainly intended to provide gyroscopic stabilisation. 
Many communications satellites use momentum wheels to manage day to day rotational position keeping in 3 axes. If there is a consistent bias from some source (eg solar wind or orbital drag or ....) then a point may be reached where a momentum wheel can no longer be accelerated. At this point the wheel is "despun" while  thrusters (usually small chemical rockets ) are used to impart opposing spin. This "rests" the wheel to its rest position so the procedure can be repeated.
Wheel spin/despin energy can be sourced from eg solar panels so no fuel is used. 
The advantage of using a MW and thrusters is that if there is usually "dither" in the momentum changes the wheel may be accelerated or decelerated as required with no long term use of chemical fuel. Also, firing the thrusters only occasionally reduces "restarts", allows the thruster to be operated in optimum operating area and generally improves (reduces) net fuel use. Exhaustion of fuel is often a factor in communications satellite lifetimes. 

Reaction Wheels aboard Kepler from - excellent page. 

Video - Single wheel inverted balancing pendulum using reaction wheel - quite impressive. 
Many images and linked pages
Video Student demonstration of a nano-satellite system reaction wheel system - not without problems :-).
Rockwell Collins - Buy yours here - no price given, but :-(.
Cubli -  a walking balancing cube
