How to rotate the origin of rotation of a quaternion

Question

Im working with a quaternion, and its roll pitch and yaw are based on its global location(Im not actually sure how quaternions work, im guessing its on fixed axis). So when i get the values they are always fixed in a certain direction, the "0" of yaw is in some fixed direction. What i would like to do is kind of "reset" the rotation so that its "0" is pointing to the direction directly in front of me and that all rotations from that point will be based on the "0" being the direction i was initially facing. How do i do this?

Example:
     ^---say this is the original origin or "0" of the rotation.
  <     >
     v

Then if i am facing down:
     ^
  <     >
     v---I would then like this to be the new origin or rotation.

Answer 1

Turns out i just had to invert the quaternion i wanted as the new origin and multiply the current quaternion.