We classify localising subcategories of the stable module category of a
finite group that are closed under tensor product with simple (or, equivalently
all) modules. One application is a proof of the telescope conjecture in this
context. Others include new proofs of the tensor product theorem and of the
classification of thick subcategories of the finitely generated modules which
avoid the use of cyclic shifted subgroups. Along the way we establish similar
classifications for differential graded modules over graded polynomial rings,
and over graded exterior algebras.Comment: 37 pages; minor changes from the first version. This is slated to
appear in the January 2012 issue of Annals of Math., volume 175, no.
