Yes. The following tag creates an instance of a custom type named ShoppingCart and assigns it session scope (that is, it creates a unique ShoppingCart instance for each and every session created on the server):
<object id="MyShoppingCart" class="ShoppingCart" scope="session" runat="server" />
Managed types created this way are identified by class name. Unmanaged types (COM classes) are identified by CLSID or ProgID.