As announced in the introduction, our purpose is to extend our analysis of the Morita equivalences between blocks to the so-called Rickard equivalences (see Section 18 below), where one considers the derived categories (cf. [30]) or, more generally, the homotopy categories of the corresponding categories of modules (see our comment in 1.11 above and 10.7 below) instead of the categories of modules themselves. In both cases, we have to extend our arguments to the differential Z-graded O-modules and, consequently, we have to deal with the so-called differential Z -graded O-algebras, obviously with some finite group involved. It is well-known by the specialists that one way of describing these objects is to consider both the differential action and the projectors of the Z-graduation as coefficients in an extended coefficient ring D (no longuer commutative!), which is a fortiori an O-algebra not finitely generated as O-module. However, since Rickard equivalences depend on differential Z-graded O-modules which are actually finitely generated as O-modules (see [31] or 18.2 below), we are in fact interested in the quotients of D which are so.