  For the bosonic string on the torus we compute boundary states describing
branes with not trivial homology class in presence of constant closed and open
background. It turns out that boundary states with non trivial open background
generically require the introduction of non physical ``twisted'' closed
sectors, that only $F$ and not ${\cal F}=F+B$ determines the geometric
embedding for $Dp$ branes with $p<25$ and that closed and open strings live on
different tori which are relatively twisted and shrunk. Finally we discuss the
T-duality transformation for the open string in a non trivial background.
