  Let G be a finite group, let N be a normal subgroup of G, and let theta in
Irr(N) be a G-invariant character. We fix a prime p, and we introduce a
canonical partition of Irr(G|theta) relative to p. We call each member B_theta
of this partition a theta-block, and to each theta-block B_theta we naturally
associate a conjugacy class of p-subgroups of G/N, which we call the
theta-defect groups of B_theta. If N is trivial, then the theta-blocks are the
Brauer p-blocks. Using theta-blocks, we can unify the Gluck-Wolf-Navarro-Tiep
theorem and Brauer's Height Zero conjecture in a single statement, which, after
work of B. Sambale, turns out to be equivalent to the the Height Zero
conjecture. We also prove that the k(B)-conjecture is true if and only if every
theta-block B_theta has size less than or equal the size of any of its
theta-defect groups, hence bringing normal subgroups to the k(B)-conjecture.
