  We provide a description of the orbit space of a sheet S for the conjugation
action of a complex simple simply connected algebraic group G. This is obtained
by means of a bijection between S/G and the quotient of a shifted torus modulo
the action of a subgroup of the Weyl group and it is the group analogue of a
result due to Borho and Kraft. We also describe the normalisation of the
categorical quotient \overline{S}//G for arbitrary simple G and give a
necessary and sufficient condition for S//G to be normal in analogy to results
of Borho, Kraft and Richardson. The example of G_2 is worked out in detail.
