\centerline{\large {\cs k}*\-Fusion Algebra and Alperin's Conjecture}
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\centerline{by}  
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\centerline{LLUIS PUIG}
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\centerline{\cds CNRS, Universit\'e Paris
7,\quad 6 Av Bizet, 94340 JOINVILLE-LE-PONT, FRANCE,\quad
}

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£1. In a lecture with almost the same title --- at the 2002 Durham 
Symposium ---
Markus Linckelmann made a claim for the existence of a suitable 
$k^*\-$extension of
the full subcategory of the {\it Brauer category\/}  of a block over 
the set of all
its {\it selfcentralizing Brauer pairs\/}, relating the $k\-$algebra 
associated with
this extension to Alperin's Weight Conjecture on the number of 
modular irreducible
characters in the block.
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£2. The purpose of this short Note is to explicit our comment at the 
end of this
lecture,