Page:

<apex:page>
    <c:resellerAccountSearch />
</apex:page>

Component:

<apex:component controller="resellerAccountSearch" >
 <apex:form >
  <apex:pageblock > 
   
   <apex:inputText value="{!searchValue}" id="searchtext"/>
   <apex:commandButton value="Search" action="{!search}" rerender="results" status="search"/>
   <br/>
   
   <!-- This check box works fine but if it is in the header section below it doesn't work
   <apex:inputCheckBox value="{!selectAllCheckbox}"> 
    <apex:actionSupport event="onclick" action="{!selectAll}" rerender="results"/>
   </apex:inputCheckBox> -->
   
   <apex:actionStatus id="search">
   
    <apex:facet name="start">
     <strong>Retrieving data... </strong>
    </apex:facet>
    
    <apex:facet name="stop">

     <apex:pageblockTable value="{!cAccounts}" var="c" id="results">
      <apex:column >
       <apex:facet name="header">
        <apex:inputCheckBox value="{!selectAllCheckbox}"> 
         <apex:actionSupport event="onclick" action="{!selectAll}" rerender="results"/>
        </apex:inputCheckBox>
       </apex:facet>
       <apex:inputCheckBox value="{!c.selected}"/>
      </apex:column>
      <apex:column value="{!c.acct.Name}"/>
      <apex:column value="{!c.acct.BillingCity}"/>
      <apex:column value="{!c.acct.CreatedDate}"/>
      <apex:column value="{!c.acct.LastModifiedDate}"/>
      <apex:column value="{!c.acct.Id}"/>
     </apex:pageblockTable>
    
    </apex:facet>
   </apex:actionStatus>
  </apex:pageblock>
 </apex:form>
</apex:component>

Controller:

public class resellerAccountSearch {
  
 public String searchValue {get; set;}
 public List<Account> results {get; set;}
 public List<cAccount> cAccounts {get; set;}
 public Boolean selectAllCheckbox {get; set;}
 
 //Constructor
 public resellerAccountSearch(){
  results = new List<Account>();
  cAccounts = new List<cAccount>();
 }
 
 public PageReference search(){
  results.clear();
  cAccounts.clear();
  
  if(searchValue.length() > 1){
      searchValue = '*'+searchValue+'*';
  
         List<List<SObject>> searchList = [FIND :searchValue IN NAME FIELDS RETURNING Account(Id, Name, BillingCity, CreatedDate, LastModifiedDate order by LastModifiedDate desc )]; 
         results = ((List<Account>)searchList[0]);
         
         for(Account acct: results){
          cAccounts.add(new cAccount(acct)); 
         }
  }
  return null; 
 }
 
 public PageReference selectAll(){
  system.debug(selectAllCheckbox);
  for(cAccount acct : cAccounts){
   system.debug(acct.selected);
   
   if(selectAllCheckbox == true){
    acct.selected = true;
   }else{
    acct.selected = false; 
   }
  }
  return null; 
 }
 
 public class cAccount{
  public Account acct {get; set;}
  public Boolean selected {get; set;}
  
  public cAccount(Account a){
   this.acct = a; 
   selected = false;
  }
 }

}