Rotate object having animations is it possible on Blender to rotate an object with its animations ? 

As a proof of concept, i bought an character with animations. Then i tried to rotate the whole object and the result was strange.
I assume that it's just a bug when modeling/skinning/rigging the character but not so sure. What may cause this bug ?
You could try parenting the character rig to something else, maybe an empty or a non-printing object, that is centered right at the base of the rig. Then rotate that parent object, and everything should be good.

Actually, rigs often have a base object included. Check to see if your character's rig already has a base or handle that everything else is parented to. Then instead or rotating the whole character, just rotate the base. You should get better result.