NEW YORK – Blackstone Group LP, the world’s largest private-equity firm, is allowing retail investors a piece of the action.

The New York-based buyout shop announced plans this past week to raise $4 billion through an initial public offering. Blackstone, which uses its own investors’ money to buy shareholder-owned companies and take them private, could be valued by some $40 billion once it goes public.

The buzz about an IPO has been escalating since word leaked out more than a week ago. But some observers are questioning the deal because it still gives retail investors little say in companies operated by private concern. Blackstone plans to sell shares in its underlying management company, and not the side of the company that runs its investment portfolio. It will offer a limited partnership for investors.

The IPO now gives retail investors entry into private equity. Buying into Blackstone gives investors a piece of an investment management firm whose portfolio includes everything from Madame Tussaud’s wax museums to a massive stake in Germany’s Deutsche Telekom.

And many investors have much faith in the firm. In less than six years, total assets have risen more than fivefold, from $14 billion to $78 billion.