From your specs, I'm kind of assuming you are aiming for a DDD based implementation
First, some assumptions to help map this to more common terminology: I assume your "Business Rules" layer is just used by your activity layer, and thus can be considered as part of the domain layer.
You mention business objects. I assume then that you have a domain layer. This might be your "activity layer". This should be the layer that knows how to update objects and return them to the service layer.
The service layer (or "application layer" in DDD terms) should be mapping the DTOs, and invoking domain services. MS has a decent diagram here. But basically the workflow should be:
- Send DTO to service layer
- Service layer invokes DTO adapters to create domain objects/entities out of DTOs.
- Service layer invokes domain services to perform business logic (invokes rules)
- Domain services update domain objects as a result of business rules
- Persistance layer is invoked by domain services as needed
- Domain services return updated domain objects to service layer
- Service layer maps domain objects back to DTO and returns them
There are of course many variations on this theme, but this should be your starting point.