I know kinetic energy is due to motion of an object. But what if, I, the observer of an object is moving and that object appears to be moving for me, then which one has kinetic energy. is it me or that object?I mean the object doesn't actually move but it appears to be moving because I am moving.
Kinetic energy depends on the reference frame of an observer. Therefore, kinetic energy is not a property of an object only: If you are moving along with an object and you define yourself as reference, then the kinetic energy of the object is zero (in this special reference frame).
The English Wikipedia article on Kinetic Energy has a section "Frame of reference" where this is explained in detail.