LAUSR

In this paper, by using the notion of convolution types we introduce symmetric and non-symmetric convolution type $$\hbox {C}^*$$ -algebras. It is shown that any (exact) convolution type induces a (an exact) functor on the category of $$\hbox {C}^*$$ -algebras. In particular, any group induces a convolution type and a functor on the category of $$\hbox {C}^*$$ -algebras. It is also shown that discrete crossed product of $$\hbox {C}^*$$ -algebras and discrete inverse semigroup $$\hbox {C}^*$$ -algebras can be considered as convolution type $$\hbox {C}^*$$ -algebras.