Why does my cat roll over onto her back exposing her belly?

When a cat rolls over onto her back to expose her belly it looks as if she wants her belly rubbed. It may be true that she does want her belly rubbed for awhile, but it should not be overdone, but the more likely reason for this is that your cat is presenting to you a submissive position which is linked to a greeting.

I believe it is a sort of combination action: both a greeting, a submission, and a possible request for her tummy rub which in effect will be an exchange of scent from you to her and vice versa. Scent exchange is also part of a friendly greeting and it makes the place, the home, more friendly for the cat.

However, underpinning this particular behaviour is this submissive position which is indicative of the fact that the cat sees us as the dominant partner.

As mentioned, stroking cats really should be done gently and the amount of it should be limited. The cat might like it but after awhile she may change her mind because it is a position of great vulnerability for a cat which can make her feel slightly anxious and the anxiety clicks in after a while overcoming the pleasure she receives from the stroking.