What happens with Fortinbras at the end of Hamlet?

The play of Hamlet comes full circle
with the end of Act 5 and Fortinbras's arrival at the Danish court.  In Act 1 we hear
about his plans to try to attack Denmark in order to regain the lands lost by his father
to King Hamlet many years earlier.  In Act 5, Fortinbras is in Denmark on his return
from a battle in Poland.  When he arrives at the court he is confronted with the sight
of four dead bodies:  King Claudius, Queen Gertrude, Laertes, and Prince Hamlet.  It
would seem that with no one in the royal family to take the throne, it is going to come
to Fortinbras by default.  It is actually Hamlet's final words that help to solidify
this result.  He tells Horatio that he "sets his election lights on Fortinbras."  As
Denmark is an elected monarchy, this will help ensure that Denmark is left in the hands
of a royal person whom Hamlet knows is capable of decisive action (as we learn from
Hamlet's reaction to seeing him back in Act 4.)  Fortinbras hears the story of how these
deaths came to be from Horatio, and Fortinbras responds with the fact that "it is with
sorrow (for all the needless death) I embrace my fortune."  He solidifies the justice of
his taking the crown when he says, "I have some rights of memory in this kingdom / Which
now to claim my vantage doth invite me."  Fortinbras acknowledges that Hamlet may have
been a good king had be had throne, and he ensures that Hamlet will be given a funeral
fitting a king.  The only problem with all of this is that now Denmark is the hands of a
foreign ruler.  What Hamlet was trying to do -- rid the Danish throne of corruption and
evil -- is done, but the results are not what anyone would have
wished.