Mechanics of Clifford Algebra valued Möbius Maps

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The Möbius maps

$$ (ax+b)(cx+d)^{-1} $$

Where $a,b,c,d,x \in \mathbb{C}$ are well-understood, but how do the ones where the variable and coefficients are in Clifford Algebras act?

Are there any good resources for further reading on this?