  Recently, G. Navarro introduced a new conjecture that unifies the Alperin
Weight Conjecture and the Glauberman correspondence into a single statement. In
this paper, we reduce this problem to simple groups and prove it for several
classes of groups and blocks. Our reduction can be divided into two steps.
First, we show that assuming the so-called Inductive (Blockwise) Alperin Weight
Condition for finite simple groups, we obtain an analogous statement for
arbitrary finite groups, that is, an automorphism-equivariant version of the
Alperin Weight Conjecture inducing isomorphisms of modular character triples.
Then, we show that the latter implies Navarro's conjecture for each finite
group.
