Bases for certain varieties of completely regular semigroups

Completely regular semigroups equipped with the unary operation of inversion within their maximal subgroups form a variety, denoted by CR. The lattice of subvarieties of CR is denoted by L(CR). For each variety in an boolean AND-subsemilattice Gamma of L(CR), we construct at least one basis of identities, and for some important varieties, several. We single out certain remarkable types of bases of general interest. As an application for the local relation L, we construct L-classes of all varieties in Gamma. Two figures illustrate the theory.