Before you select one of these topics, read Crystal page 309: you may find a topic that you like better (or a way of making one of the ones below as precise as possible).
Account for, from a(n) historical point of view, one of the following sets of "equivalent lexical items" in North American and British English. A good chunk of your report should consist of a description and explanation of semantic overlap/change in earlier English.
You should consult some reputable and modern dictionaries of British and North American English as well as the OED, in order to make sure that you've got the PDE meanings down. You may also find that the "division" isn't strictly regional, so see what's there.