package My::CGI;

use strict;
use CGI;

sub new {
   my $class = shift;
   my $foo   = 'bar';
   my $q     = CGI->new();
   my $self = {
      foo => "$foo",
      cgi => "$q",
   };
   return bless $self, $class;
}

package main;

use strict;

my $q = My::CGI->new();

print $q->{foo}, "\n";
print $q->{cgi}->a({href=>'http://foo.bar'},'some link'),"\n";

__END__
yields:
bar
Can't locate object method "a" via package "CGI=HASH(0x80f8a20)"
at ./foo.pl line 26.