In this paper we construct non-negative gradings on a basic Brauer tree algebra AΓ corresponding to an arbitrary Brauer tree Γ of type (m,e). We do this by transferring gradings via derived equivalence from a basic Brauer tree algebra AS
Nearby in the stack
, whose tree is a star with the exceptional vertex in the middle, to
AΓ
. The grading on
AS
comes from the tight grading given by the radical filtration. To transfer gradings via derived equivalence we use tilting complexes constructed by taking Green's walk around
Γ
(cf. [Zak]). By computing endomorphism rings of these tilting complexes we get graded algebras. We also compute
OutK(AΓ)
, the group of outer automorphisms that fix isomorphism classes of simple
AΓ
-modules, where
Γ
is an arbitrary Brauer tree, and we prove that there is unique grading on