  We present a general theory of braided quantum groups in the C*-algebraic
framework using the language of multiplicative unitaries. Starting with a
manageable multiplicative unitary in the representation category of the quantum
codouble of a regular quantum group $\mathbb{G}$ we construct a braided
C*-quantum group over $\mathbb{G}$ as a C*-bialgebra in the monoidal category
of the $\mathbb{G}$-Yetter-Drinfeld C*-algebras. Furthermore, we establish the
one to one correspondence between braided C*-quantum groups and C*-quantum
groups with projection. Consequently, we generalise the bosonization
construction for braided Hopf-algebras of Radford and Majid to braided
C*-quantum groups. Several examples are discussed. In particular, we show that
the complex quantum plane admits a the braided C*-quantum group structure over
the circle group $\mathbb{T}$ and identify its bosonization with the simplified
quantum $E(2)$ group.
