virtual operator +

Hi

I ws wondering if there is a way to implement operator+ in case of
virtual classes.
Here's the problem. I have to have a base string class from which two
classes (normal char string and a hash string class ) are derived. The
two derived classes are template classes specifying the sizes. The
base class is a non-template class so that it can be used generically
in the interface classes. the design would look like

class Base_string {
          };

template<size>
class Char_string : Base_string {
                                           };

template<size>
class Hash_string: Base_string{
                                        };
So that in the interface class of the application he can use just the
generic Base_string to access the functions and doesnt have to know
whether its a Char or hash string
The issue is in implementing the operator+ . Since all the methods are
virtual in the base class and it should call the desired methods
polymorphically, operator+ is a challenge as it returns a Base_string
object
So if I have something like
Char_string<24> char_string1("Hello");
Char_string<24> char_string2("world");
Char_string<24> char_result;
Base_string* base_a = &char_string1;
Base_string* base_b = &char_string2;
Base_string* base_r = &char_result;

i wouldnt be able to do
*base_r = *base_a + *base_b; as the operator+ would return a
Base_object?
Any soultions to the above issue is most welcome