Linear source invertible bimodules and Green correspondence

We show that the Green correspondence induces an injective group homomorphism
from the linear source Picard group L(B) of a block B of a nite group algebra
to the linear source Picard group L(C), where C is the Brauer correspondent of
B. This homomorphism maps the trivial source Picard group T (B) to the trivial
source Picard group T (C). We show further that the endopermutation source Picard
group E(B) is bounded in terms of the defect groups of B and that when B has a
normal defect group E(B) = L(B). Finally we prove that the rank of any invertible
B-bimodule is bounded by that of B.