  In this note we show that the multiplicative Grothendieck-Springer space has
a natural quasi-Poisson structure. The associated group-valued moment map is
the resolution morphism, and the quasi-Hamiltonian leaves are the connected
components of the preimages of Steinberg fibers. This is a multiplicative
analogue of the standard Poisson structure on the additive
Grothendieck-Springer resolution, and an explicit illustration of a more
general procedure of reduction along Dirac realizations which is developed in
recent work of the author and Mayrand.
