  In this paper we describe an algebraic/geometrical approach to quantum
scrambling. Generalized quantum subsystems are described by an hermitian-closed
unital subalgebra $\cal A$ of operators evolving through a unitary channel.
Qualitatively, quantum scrambling is defined by how the associated physical
degrees of freedom get mixed up with others by the dynamics. Quantitatively,
this is accomplished by introducing a measure, the geometric algebra
anti-correlator (GAAC), of the self-orthogonalization of the commutant of $\cal
A$ induced by the dynamics. This approach extends and unifies averaged
bipartite OTOC, operator entanglement, coherence generating power and Loschmidt
echo. Each of these concepts is indeed recovered by a special choice of $\cal
A$. We compute typical values of GAAC for random unitaries, we prove upper
bounds and characterize their saturation. For generic energy spectrum we find
explicit expressions for the infinite-time average of the GAAC which encode the
relation between $\cal A$ and the full system of Hamiltonian eigenstates.
Finally, a notion of ${\cal A}$-chaoticity is suggested.
