Styx Lawsuit -- We Were CHEATED ... By Evil Record Company Plot

Styx -- one of the greatest rock bands ever -- says a record company concocted an elaborate scheme to CHEAT the band out of major royalty payments for YEARS ... all so the company could pocket the dough itself, this according to a new lawsuit.

The band -- who had major hits like "Lady" and "Come Sail Away" -- filed the lawsuit under its corporation Gelderdisk LTD in Los Angeles County Superior Court Friday, against music giant A&M Records.

In the docs, Styx says A&M has purposefully been shorting the band royalty income earned from digital downloads and ringtones -- and did so by concocting a "phony business model" in order to "avoid its royalty obligations."

Specifically Styx claims for every ONE dollar the band's been paid over the years "it should have been paid, or credited anywhere between TWO and FIVE dollars."

Styx is suing for unspecified damages -- to be proven at trial -- but based on the band's success over the last three decades ... it probably has a pretty big number in mind.