[Tex/LaTex] Define strange operators

Question

I' looking for a symbol rendering the connected sum of $n$ topological spaces (or other quite strange topological operations) in a "product-like" manner… What For example in writing

$$
{\Large{*}}_{i=1}^n G_i
$$

for the free product of n groups. How can I render this with the # operation in topological spaces? (Yes, I'm studying Hatcher's AT…)

Edit: (Some mind-reading clarification by Willie)

The OP is not asking about how to use the * or \ast symbols, if I read him correctly. He is asking the following question:

How to define a (possibly variable size) math operator like \sum and \prod where the operator symbol is the octothorpe #, such that for in-line maths the upper and lower limits follow next to the symbol, and in \displaystyle with the upper and lower limits above and below the symbol?

This seems to be the referred part of Hatcher’s AG:

Answer 1

The \mathop{..} command from amsmath makes its argument behave like a "large operator".

 \documentclass{article}
 \usepackage{amsmath}
 \usepackage{relsize}

 \newcommand{\bigstar}{\mathop{\Huge \mathlarger{\mathlarger{*}}}}

 \begin{document}

 Display:

 \[ \bigstar_{x}^{y} \]

 Inline: \( \bigstar_{x}^{y}\)


 \end{document}