Parts Included on a brand new Coleman Furnace DGAA077DBTB?

I had a Coleman furnace model DGAA077DBTB installed back in January and we have been having problems since a month after. The guy who installed it is saying that we need to buy a flue pipe (smoke stack). Wouldn't that be included when you buy a $2,200.00 brand new furnace? Please help!! We also had a guy come out last friday and he said that he had to shut off and tear down our furnace due to inproper installation and Carbon Monoxide could be leaking into our home. I need to know whether the flue pipe should have come with our furnace. Please advise. Thanks!! :)