As some major Walgreen (WAG) investors urge the largest U.S. pharmacy to move its corporate headquarters to Europe, some activists are claiming such a move would cost taxpayers billions of dollars. 

Americans for Tax Fairness and Change to Win Retail Initiatives issued a report Wednesday alleging that the HQ move, a tax-saving maneuver known as corporate inversion, could cost U.S. taxpayers $4 billion in lost revenue over five years.

A rally of a few dozen representatives from these organizations and other Chicago-based “community, labor and tax groups” was held outside of Walgreen’s flagship Chicago store Wednesday morning in coordination with these efforts. 

“If Walgreens relinquished its Illinois roots by becoming a Swiss company, it would not only be a betrayal of the people of our great state, but it would undermine critical taxpayer-funded services that we all rely on,” said William McNary, Co-Director of Citizen Action/Illinois.

The Financial Times reported in April that major investors, including Goldman Sachs (GS) and hedge funds Jana Partners, Corvex and Och-Ziff, are urging Walgreen to move its headquarters from Illinois to Switzerland to save costs.

Some reports by analysts have estimated that Walgreen’s tax rate could be cut to as little as 20% from 31% currently if it moved abroad.

Companies are legally allowed to participate in tax inversion when at least 20% of their stock is owned outside of the U.S. Walgreen would likely meet that criteria upon the closing of its purchase of European pharmacy giant Alliance Boots, slated for early 2015.

The rally and report come about a month after minor Walgreen investor, CtW Investment Group, claimed tax inversion would be “detrimental” to investors, benefiting short-term players and hurting long-term investors, many of which are based in the U.S.

Shares of Walgreen were down 0.48% to $74.38 in recent trade. They are up nearly 30% since January.

Follow Jennifer Booton on Twitter at @Jbooton