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1* Introduction. We present a "generic" C*-algebra in illustration of several peculiar phenomena that may occur in the theory of representations. Let F2 denote the free group on two generators. If π is the universal unitary representation of F2 on a Hubert space £ίf, then the full group C "-algebra C*(F2) is the C*-subalgebra of ^ ( < a r ) generated by the set {π(g):geF2} (see [4, §13.9]). Alternatively, we can re-define C*(F2), in an operator-theoretical setting, as follows:

The fullC∗-algebra of the free group on two generators

The fullC^∗-algebra of the free group on two generators