  We define and systematically study nonassociative C*-algebras as C*-algebras
internal to a topological tensor category. We also offer a concrete approach to
these C*-algebras, as G-invariant, norm closed *-subalgebras of bounded
operators on a G-Hilbert space, with deformed composition product. Our central
results are those of stabilization and Takai duality for (twisted) crossed
products in this context.
